Petty was a younger son of Sir William Petty and Elizabeth, Baroness Shelburne, daughter of Sir Hardress Waller. He succeeded his elder brother Charles Petty, 1st Baron Shelburne to the family estates in 1696 and then bought further estates near Wycombe, Buckinghamshire.
Petty was elected to the Irish House of Commons for Midleton in 1692, a seat he held until 1693, and then represented County Waterford between 1695 and 1699. The latter year the barony of Shelburne which had become extinct on the early death of his elder brother in 1696 was revived in his favour. Two years later he was sworn of the Irish Privy Council. He was later a member of the British House of Commons for Great Marlow between 1715 and 1722 and for Wycombe between 1722 and 1727.  In 1719 he was further honoured when he was made Viscount Dunkerron and Earl of Shelburne in the Peerage of Ireland.
Lord Shelburne married the Hon. Arabella, daughter of Charles Boyle, 3rd Viscount Dungarvan, in 1699. There were no surviving children from the marriage. The Countess of Shelburne died in October 1740. Lord Shelburne survived her by eleven years and died in April 1751, aged 75, when his titles became extinct. His estates devolved on his nephew John FitzMaurice, who changed his surname to Petty and in whose favour the earldom of Shelburne was revived in 1753 (see Marquess of Lansdowne).
- "PETTY, Henry, 1st Baron Shelburne [I] (1675-1751), of Wycombe, Bucks". History of Parliament Online. Retrieved 15 August 2018.
- "leighrayment.com Irish House of Commons 1692-1800". Archived from the original on 1 June 2009. Retrieved 11 December 2009.
- leighrayment.com Peerage: Severn to Sligo
- leighrayment.com Privy Counsellors - Ireland
- thepeerage.com Henry Shelburne, 1st Earl of Shelburne
|Parliament of Ireland|
| Member of Parliament for Midleton
With: Thomas Brodrick
St John Brodrick
| Member of Parliament for County Waterford
With: John Mason
Sir John Mason
|Parliament of Great Britain|
Sir James Etheridge
| Member of Parliament for Great Marlow
With: George Bruere
Sir John Guise, Bt
Sir Thomas Lee, Bt
| Member of Parliament for Wycombe
With: Charles Egerton 1722–1725
Hon. Charles Colyear 1726
Harry Waller 1726–1727
|Peerage of Ireland|
|New creation|| Earl of Shelburne