He was a nephew of the Lord Mayor of London Richard Saltonstall (1517–1600), and was admitted pensioner at Clare College, Cambridge in 1603. Before leaving England for North America, he served as a Justice of the Peace for the West Riding of Yorkshire and was Lord of the Manor of Ledsham. He was one of the grantees of the Massachusetts Company and left England on 26 August 1629 aboard the Arbella. He was named First Assistant to Governor John Winthrop.
Saltonstall arrived in Massachusetts with his wife, Elizabeth, and his children, Richard, Jr., Samuel, Robert, Henry, Grace, Rosamund, John, and Anne. The illness of one of his daughters caused him to return to England in 1631, along with his wife, daughters, and two of his sons. He maintained an interest in the colonies and was one of the patentees of the Connecticut Colony. In 1644, he was appointed ambassador to Holland, where his portrait was painted by Rembrandt.
Sir Richard Saltonstall appears to have been in Newtown, Montgomeryshire (Powys), Wales at the Restoration of King Charles II in 1660. On July 18, 1660 the Council of King Charles II issued an order to Sir Matthew Price, High Sheriff of Montgomeryshire to take into safe custody Vavasour Powell (described as, "a most factious and dangerous minister"), Sir Richard Saltonstall, and Richard Price of Aberbechan.
According to Sir Matthew Price's letters to Secretary Sir Edward Nicholas, Vavasour Powell, Sir Richard Saltonstall and Richard Price were concerned in a plot to depose King Charles II. Letters were found in their possession indicating the plot extended all the way to London. By August 2, 1660 Vavasour Powell was taken into custody, while Sir Richard Saltonstall and Capt. Richard Price "had left these parts" [Montgomeryshire].
Saltonstall's first wife was Grace Kaye. They had four children: sons Richard, Robert, and Samuel, and a daughter, Grace. After his wife died in 1625, Saltonstall married Lady Elizabeth West, by whom he had two additional children, Anne and John.
There are several monuments dedicated to Saltonstall in Watertown. These include Saltonstall Park on Main Street, Watertown, and the Saltonstall Founders Memorial near the Charles River.
There is a small granite monument commemorating their settlement close to the Mt. Auburn Bridge in Cambridge, Massachusetts.
- "Sir Richard Saltonstall". Massachusetts Bay First Settlers. Winthrop Society. Retrieved 2012-09-18.
- DNB has 1658
- "Saltonstall, Richard (SLTL603R)". A Cambridge Alumni Database. University of Cambridge.
- The Founders: Portraits of Persons Born Abroad Who Came to the Colonies in North America Before the Year 1701, Charles Knowles Bolton, The Boston Athenaeum, 1919
- Curtin, D. "The Winthrop Fleet of 1630". Retrieved 2007-11-30.
- Browning, Charles Henry.  "The Magna Charta Barons and Their American Descendants" p.313
- Green, Mary Ann Everett, Ed. (1860). Calendar of State Papers, Domestic Series, of the Reign of Charles II 1660-1661. London: Longman, Green, Longman, and Roberts. pp. 123, 135.
- Green, Mary Ann Everett (1860). Calendar of State Papers, Domestic Series, of the Reign of Charles II 1660-1661. London: Longman, Green, Longman and Roberts. pp. 135, 176.