Gorham was born in Charlestown, Massachusetts. He took part in public affairs at the beginning of the American Revolution, was a member of the Massachusetts legislature from 1771 until 1775, a delegate to the Provincial congress from 1774 till 1775, and a member of the Board of War from 1778 until its dissolution in 1781. In 1779 he served in the State constitutional convention. He was a delegate to the Continental Congress from 1782 until 1783, and also from 1785 until 1787.

For several months in 1787, he served as assistant President of the United States Constitutional Convention when George Washington was unable to perform those duties. He worked hard to see that the United States Constitution was approved in his home state.

In connection with Oliver Phelps he purchased from the state of Massachusetts in 1786 an immense tract of land on Genesee River, for the sum of $1,000,000 (the"Phelps and Gorham Purchase"). This had been previously ceded to Massachusetts from the state of New York. They soon extinguished the Indian title to a part of this territory, surveyed it into tracts, laid out townships, and sold large parts to speculators and settlers. In 1790 they had sold nearly all their property, and, being unable to fulfill their contract in full to Massachusetts, Phelps and Gorham compromised and surrendered that portion of the land which remained under the Indian title. It was eventually acquired by Robert Morris, who resold most of it to The Holland Land Company and The Pulteney Association. Morris also kept 500,000 acres for himself, known as The Morris Reserve.