He was the son of the noted divine Gilbert Burnet and Mary Scott, born at the Hague in the Netherlands in March of 1688. He was the godson of William (later King William III) and Mary. He was an excellent but undisciplined scholar who entered Oxford at the age of 13, but was dismissed for disciplinary reasons. His later education came from private tutoring (including Isaac Newton as a tutor), and he was ultimately admitted to the bar.
With friends in the government, he was appointed the Comptroller of Customs in England before his terms as a colonial governor. He was married twice. His first wife was the daughter of Dean Stanhope and she died in 1717. He married again in New York to Anna Maria Van Horne, the daughter of Abraham and Mary Van Horne.
Governor of New York
Burnet was a capable adminstrator and better than the average colonial governor, although his tenure was not without disputes. He was apppointed governor of New York and New Jersey in the spring of 1720, and arrived in New York City on September 16 of that year. His most important accomplishment as governor was to strengthen the colony's position on the frontier.
Governor Burnet encourage direct trade with Indian tribes to reduce the influence of French traders. Along with this initiative, he strengthened outposts like Fort Oswego. This was an effective strategy. Many of the goods bartered with the Indians for furs were produced locally, while the French imported theirs so the colonists could undercut French prices.
He convened a meeting at Albany in 1722 of representatives from several colonies, that resulted in peace with Indian tribes for several years.
But, the costs of actions earned opposition from establishment forces, like the DeLancey family. (It also interfered with their profits from selling good to French fur traders). He also establshed the Courts of Chancery in 1727 and was censured by the assembly. The crown replaced him in 1728, not for this dispute but to make room for John Montgomerie who was favored by King George II He was reassigned as governor of Massachusetts and New Hampshire and left New York on April 15 when his replacement arrived.
Governor of Massachusetts
He continued a dispute with the assembly over the issue of the governor's salary since he lived on this income. Shortly into his administration, he died from a stroke in Boston on September 7, 1728.