He emigrated from England to Concord, Massachusetts, in New England in 1634 with his father William, his mother Grace and his two brothers Jeremiah and Joshua. In 1638, he and his father and brother moved to Stratford, Connecticut, being among the first Europeans to arrive at that place. Joseph Judson became so prominent in the development of the town and his name so frequent in the records that historians thought he was the first of the name in Stratford. He was elected as a freeman in 1658. He was elected a Deputy in 1659 and served in the workings of the Colony of Connecticut for the next thirty years. In 1671, he received permission from then Governor John Winthrop, Jr. to create a new town called Woodbury and removed from Stratford with other families to settle the newly created town the same year. Judson had a disagreement with Joseph Hawley and the majority of elders at Stratford as they tried to introduce the half way covenant. This led to a major rift which lasted for many years and split the church and the town.
On 24 October 1644, Judson married Sarah Porter who was born 15 Mar 1624 in Felsted Essex England. She was the daughter of John Porter and Anna (Rosanna) White of Windsor, Connecticut. They raised eleven children.
In November 1660, Judson inherited the stone house that had been built by his father ca. 1639 on Academy Hill in Stratford. He maintained a farm on Mischa Hill located in the present-day village of Nichols in the town of Trumbull. His son John inherited the farm and sold part of it to Abraham Nichols in 1696 at which time it was described as Lt. Joseph Judson's old farm and the parcel had a barn on it. In 1662, Judson and his brother Jeremiah inherited their father's iron works located near Stony River in New Haven, Connecticut.
- Sarah, born 1645, married Edmund Howell in 1688 and raised three children in Southampton, New York.
- John, born 1647, married Elizabeth Chapman in 1674 and raised ten children, second wife Hannah Hawkins, third wife Mary Tudor in 1699 and raised four children. Original founder of Woodbury.
- Captain James, born 1650, married Rebecca Welles in 1680, granddaughter of Connecticut Colony Governor Thomas Welles and raised nine children in Stratford.
- Grace, born in 1651, married Samuel Prudden in 1669 and raised five children in Milford, second husband Thomas Clark and had one more child.
- Joseph, born in 1654, raised seven children in Stratford.
- Hannah, born in 1657, married Samuel Wadsworth in 1680 and raised three children in Farmington.
- Esther, born in 1660, married Benjamin Curtiss in 1680 resided in Trumbull and raised ten children.
- Joshua (twin), born in 1664, died young.
- Ruth, (twin), born in 1664, married Samuel Welles in 1688, grandson of Connecticut Colony Governor Thomas Welles and raised six children in Hartford.
- Phoebe, born in 1666, married Thomas Uffoot (Ufford) in Stratford.
- Abigail, born in 1669, married Josiah Curtiss in 1692 and raised four children in Stratford.
- Gerald R. Ford (1913–2006), 38th President of the United States, 7th great grandson
- Captain David Judson, grandson through Captain James.
Judson was instrumental in negotiating or trading with and buying large tracts of land from the Native American tribe named the Golden Hill Paugussett Indian Nation. The Paugussett's had resided in Connecticut as a self-sustaining community for several thousand years before the English arrived at Stratford in the late 1630s. Since the first volume of Stratford land records has been lost or destroyed by fire, no written records exist prior to 1648 or 1650 to record earlier Indian deeds.
After twelve to fifteen years after the onset of the Stratford settlement, the settlement had grown so much in size that the displaced Indian Nation began to ask for compensation for land north of an east to west line 6 miles (9.7 km) north of Long Island Sound. The Stratford proprietors agreed and began to make several large purchases from the Indians.
Mohegan Hills purchase
In 1661, Judson negotiated with Amantaneag, Akenotch and Ansantaway of the Paugussett Indians for a large tract of land known to the English as Mohegan Hills and to the Indians as Ackquunokquahou. The land was situated between the two branches of the Farmill River and was 5,000 acres (20 km2) in size and was bounded on the northwest by the lower part of Moose Hill and the south with Trap Falls. The land is located in what is now the towns of Shelton and Monroe.
This purchase led to a disagreement with the Stratford selectmen and the town petitioned the Court at the Colony of Connecticut to settle differences with Judson over the ownership of the land. The Court appointed a time to hear the matter, but it seems, according to Stratford town records, to have been amicably settled without the help of the Court by the following town record;
The Town upon ye 6th December, 1672, sufficient consideration moving thereunto doe grant and allow to Lt. Joseph Judson the peacable improvement of so much land, good and bad altogether lying at ye place commonly called ye Mohegan Hills, ye hop-garden, meadow and lowland on both sides ye East Spraine of ye Far Mill River as high on that Sprayne as this accommodation reacheth, as is the proportion of an eight acre meadowed inhabitant to ye whole bounds, with this provision that it shall not be expected to be all laid out at present but successively as other proprietors.
Long Hill purchase
In 1662, Judson negotiated a deed with the Paugussett Indians for the territory of a considerable part of what is now the townships of Trumbull, Monroe and Easton, lying west of the land which the town of Stratford had previously purchased, or west of the Pequonnock River, extending to Fairfield line and from a line crossing the township east and west about at the Trumbull Church, or possibly a little further south, then north to Newtown. This was known as the Long Hill purchase.
- May 1661, asked by the Court at the Colony of Connecticut to set the town line between the shoreline settlements of Fairfield and Stratford.
- May 1675, appointed to a committee to view the lands of Derby, Woodbury, Mattatuck, Pootatuck and Wyantenock. Judson was to measure the distance between place and place and to consider what may be suitable bounds for each town and present same to Court in October next.
- May 1678, appointed to a committee to view lands between Milford and Derby. Also moved that the Court should order inhabitants of Woodbury to settle permanently within a month or lose all rights to lands there.
- October 1680, entered signed statement and agreement of town boundary for Woodbury, Derby and Mattatuck to the Court at the Colony of Connecticut.
- May 1684, named Deputy to the Court of the Colony of Connecticut and Lieutenant of the Train Band for Woodbury.
- October 1684, named Deputy to the Court of the Colony of Connecticut for Woodbury.
- May 1685, named Deputy to the Court of the Colony of Connecticut for Woodbury. and appointed to a committee to run the line or bounds between Fairfield and Norwalk.
- October 1685, appointed Deputy for Woodbury.
- May 1686, appointed Deputy for Woodbury.
- October 1686, appointed Deputy for Woodbury.
- May 1687, appointed Commissioner for Woodbury.
- May 1689, appointed Commissioner or Justice of the Peace for Woodbury.
- In July 1665, appointed to a committee to prepare the colony against attack from the Dutch during the Second Anglo-Dutch war.
- June 1672, appointed Lieutenant of the Stratford Train Band.
- January 1675, Major Robert Treat and Major Nathan Gold asked the colony for officers in the army being raised in Fairfield County, Connecticut. Judson's name was hand written into the records by William Leete who suggested that Judson was such a suitable person. The colony was raising troops to fight against the Narragansett Indians during the King Philip's War.
- May 1676, appointed Captain of the eighty-two men raised in Fairfield County should Captain Jonathan Silleck be disinabled. Each soldier was ordered to have a pound of powder and three pounds of bullets and were to assemble at Norwich, Connecticut 27 May.
- Orcutt Vol. 1 p. 110
- A complete history of Connecticut: civil and ecclesiastical, from the emigration of its first planters, from England, in the year 1630, to the year 1764 ; and to the close of the Indian wars, Volume 1, Benjamin Trumbull, Maltby, Goldsmith and Co. and Samuel Wadsworth, 1818 
- The Public Records of the Colony of Connecticut Vol. 1 p. 315
- History of Ancient Woodbury Connecticut From the First Indian Deed 1659 to 1872, William Cothren, 1872, Vol. 2 p. 916
- History of Stratford 1639-1969, William Howard Wilcoxson, Stratford Tercentenary Commission, Stratford, Connecticut, 1939, p. 734
- Stratford Land Records Vol. 2, p. 82
- Orcutt Vol. 1, p. 111
- CTGENWEB website retrieved on 2011-04-11
- History of Ancient Woodbury, Connecticut, William Cothren, 1854, p. 61
- HMDB Historical Marker database website retrieved 2011-04-04
- Orcutt, Vol. 1, p. 22
- Orcutt Vol. 1 p. 92
- Orcutt, Vol. 1 p. 269
- Orcutt Vol. 1, p. 22
- Orcutt Vol. 1, p. 270
- Orcutt Vol., 1 p. 271
- Colonial Records of Connecticut Vol. 1 p. 367
- The Connecticut Magazine Vol. 5 p. 499, October 1899
- Colonial Records of Connecticut Vol. 2 p. 253
- Colonial Records of Connecticut Vol. 3 p. 3
- Colonial Records of Connecticut Vol. 3 p. 10-11
- Colonial Records of Connecticut Vol. 3 p. 70
- Colonial Records of Connecticut Vol. 3 p. 139
- Colonial Records of Connecticut Vol. 3 p. 156
- Colonial Records of Connecticut Vol. 3 p. 169
- Colonial Records of Connecticut Vol. 3 p. 175
- Colonial Records of Connecticut Vol. 3 p. 181
- Colonial Records of Connecticut Vol. 3 p. 195
- Colonial Records of Connecticut Vol. 3 p. 214
- Colonial Records of Connecticut Vol. 3 p. 230
- Colonial Records of Connecticut Vol. 3 p. 252
- Colonial Records of Connecticut Vol. 2 p. 21
- Colonial Records of Connecticut Vol. 2 p. 180
- Colonial Records of Connecticut Vol. 2 p. 395
- Colonial Records of Connecticut Vol. 2 p. 279
- Reverend Samuel Orcutt, A History of the Old Town of Stratford and the City of Bridgeport, Connecticut, Volume 1, Fairfield Historical Society, 1886
- Reverend Samuel Orcutt, A History of the Old Town of Stratford and the City of Bridgeport, Connecticut, Volume 2, Fairfield Historical Society, 1886
- History of Trumbull Dodrasquicentennial 1797–1972 Commemorative Book, Trumbull Historical Society, 1972
- Connecticut General Assembly, The Public records of the Connecticut Colony 1636–1776, Press of the Case, Lockwood & Brainard, 1885
- William Cothren, History of Ancient Woodbury Connecticut, Bronson Brothers, Waterbury, 1854
- Frederick Haines Curtiss, A Genealogy of the Curtiss Family, Rockwell and Churchill Press, Boston, 1903
- William Richard Cutter, New England Families, Genealogical and Memorial, Lewis Historical Publishing, NY, 1914
- Elias Sill Hawley, The Hawley Record, Press of E. H. Hutchinson & Co., Buffalo, NY, 1890