He was born in Ireland, the second, but first surviving, son of Richard Coote, third son of Sir Charles Coote, 1st Baronet, by Mary, daughter of Sir George St George. His father was created Baron Coote in 1660 (on the same day as his uncle was created Earl of Mountrath), and he succeeded his father as 2nd Baron Coote on 10 July 1683. Lord Coote was Member of Parliament for Droitwich from 1689 to 1695. He was one of the first to join the Prince of Orange in 1688, which caused him to be attainted by the Irish Parliament of King James II in May 1689. King William III and Queen Mary II, however, created him Earl of Bellomont on 2 November 1689, and granted him over 77,000 acres (310 km²) of forfeited Irish lands.
Lord Bellomont was Treasurer to the Queen from 1689 to 1693. He was commissioned as Royal Governor of Massachusetts, New Hampshire, and New York in 1697. He began his administration in New York the next spring in 1698 and did not assert his dominion over Massachusetts until May 1699, when he presided in person as Massachusetts' Governor.
Bellomont had been the primary sponsor of Captain William Kidd's charter as a privateer, and when he was charged with piracy, Captain Kidd came to Boston to enlist Lord Bellomont's support. The political tide had turned against Kidd, and Bellomont promptly had him arrested. The accused pirate was given a brief hearing and was then returned to London where he was found guilty of piracy and hanged.
Bellomont's attempt to govern three such distant territories took a toll on his health and he succumbed to a severe case of gout in 1701. He was replaced temporarily in New York by John Nanfan as Acting Governor until the arrival of Lord Cornbury in 1702 and in Massachusetts by William Stoughton, who died before Joseph Dudley arrived as Bellomont's replacement in 1702.
He married Catharine, daughter of Bridges Nanfan. His eldest son, Nanfan, Lord Coloony, succeeded to the Earldom on his death, his second son, Richard, succeeded in turn as 3rd Earl on his elder brother's death. On the 3rd Earl's death without surviving male heirs, the Earldom became extinct, while the Barony devolved on his cousin, Sir Charles Coote, who was later also created Earl of Bellomont.