The son of a clergyman, Leonard Welsted attended Westminster School (1703-07) before being admitted to Trinity College Cambridge as a pensioner in 1707. He clerked in the Secretary of State's Office and later the Ordinance Office (1725-47). Welsted married a daughter of Henry Purcell and was patronized by Bishop Hoadly; he was a friend of John Philips and Richard Steele. Pope blasted his reputation in a burlesque of Denham's famous couplets: "Flow, Welsted, flow, like thine inspirer, beer, | Tho' stale, not ripe; tho' thin, yet never clear; | So sweetly mawkish, and so smoothly dull; | Heady, not strong; and foaming, tho' not full." In 1787 John Nichols edited Welsted's works in an unsuccessful attempt to retrieve his reputation.
A poem on apple-pye. 1704.
A poem occasioned by the late famous victory of Audenard. 1709.
The Duke of Marlborough's arrival: a poem. 1709.
A poem to the memory of the incomparable Mr Philips. 1710.
Dionysius Longinus on the sublime; with some remarks on the English poets. 1712.
An epistle to Mr Steele on the King's accession. 1714.
An ode on the birth-day of the Prince of Wales. 1716.
Palemon to Caelia, at Bath: or the triumvirate. 1717.
An epistle to his Grace the Duke of Chandos. 1720.
A prologue to the town, as it was spoken at the theatre in little Lincoln's-Inn Fields. 1721.
An epistle to the late Dr Garth. 1722.
Epistles, odes, &c, written on several subjects. 1724.
Oikographia: a poem. 1725.
An ode to Major General Wade. 1726.
A hymn to the Creator, by a gentleman on the death of his only daughter. 1726.
The dissembled wanton, or my son get money: a comedy. 1727.
A discourse to Sir Robert Walpole; to which is annex'd Proposals for translating the whole works of Horace, with a specimen. 1727.
One epistle to Mr A. Pope. 1730.
Of false-fame: an epistle to the Earl of Pembroke. 1732.
Of dulness and scandal, occasion'd by the character of Lord Timon, in Mr. Pope's Epistle to the Earl of Burlington. 1732.
The scheme and conduct of providence from the creation to the coming of the Messiah. 1736.
The summum bonum: or wisest philosophy. 1741.
The works, in verse and prose, ed. John Nichols. 1787.