He was born at Tickencote, Rutland, in 1681. He matriculated at Pembroke College, Oxford, on 20 May 1698 aged 17. He was the eldest son of Eusebius Buswell, formerly Pelsant, of Lyddington, Rutland, by Frances Wingfield, daughter of Sir Richard Wingfield of Tickencote. Eusebius Buswell, Senior, was the son of Sir Eusebius Pelsant of Cadeby, Leicestershire, by his second wife Anne, the sister of Sir George Buswell, Baronet. Sir George died without issue on 10 March 1667, when Eusebius Buswell, Senior, was about 11 years old and presumably still called Pelsant. By 1706, he had adopted the surname of his maternal uncle, Buswell.
He married firstly, Hester Skrymshire, second daughter and co-heir of Sir Charles Skrymshire of Norbury, Staffordshire, by his first wife Hester Taylor, daughter and heiress of George Taylor of Darwent Hall, Derbyshire. She died without issue on 7 April 1706, and was buried at All Saints' Church, Clipston, Northamptonshire. He married secondly Honora Sneyd (baptised 23 May 1694), daughter of Ralph Sneyd, of Keel Hall, Staffordshire. They had an only daughter, Frances, who married Christopher Horton of Catton, Derbyshire.
On his death in or about 1730, the baronetcy became extinct. His estate was heavily in debt, and a private bill "for vesting certain Lands and Estates, in the Counties of Stafford, Leicester, Rutland, and Northampton, late the Estates of Sir Eusebius Buswell Baronet, deceased, in Trustees, to be sold, for the Payment of his Debts" was passed by the Parliament of Great Britain in June 1732 to enable payment.
There is a memorial tablet in All Saints' Church, Clipston, that reads "Eusebius Buswell died 1730".
- Cokayne, George Edward (1906) Complete Baronetage. Volume V. Exeter: W. Pollard & Co. LCCN 06-23564. p. 20
- "House of Lords Journal Volume 24: June 1732" Journal of the House of Lords volume 24: 1732–1737 (1767–1830), pp. 153–157
- "1731 (5 Geo. 2). c. 22", Chronological Tables of the Private and Personal Acts of the Parliaments of Great Britain Part 10 (1727–1736)
- "Church of All Saints, Clipston", British Listed Buildings. Retrieved 5 November 2012.
- Burke, John; Burke, John Bernard (1838) A genealogical and heraldic history of the extinct and dormant baronetcies, Scott, Webster, and Geary, p. 404