He was born in Brookfield, Massachusetts, the son of Dr. Jabez Upham and Katharine Nichols, and graduated from Harvard College in 1763.
In 1777, when, as a lawyer, he was required to take an oath of allegiance to the American state, he declared himself a loyalist and left for New York City to join the British.
Upham was an officer, ending the war as a major in the King's American Dragoons.
Upham, a slave-owner, voted to uphold the legality of slavery in New Brunswick in 1800 in R v Jones.
He died at the age of 66 in London, England, where he had gone to lobby the British government to make the salaries of Supreme Court judges in New Brunswick comparable with those in Upper and Lower Canada.