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.
Gorham died in Charlestown having made a fortune in real estate in the northwestern parts of Massachusetts.