Ames was born in Dedham, Massachusetts. His father died when Ames was six years old. Even though his mother did not have much money, she wanted to give Ames a good education. Ames started learning Latin when he was six years old. He went to Harvard College when he was twelve years old. He graduated in 1774. After Ames graduated, he started to work as a teacher. When he was a teacher, he also studied law. He started to work as a lawyer in the year 1781.
He served in the Massachusetts House of Representatives in 1788. He was also part of the Massachusetts Convention in the same year. He served in Congress from March 4, 1789 to March 3, 1797. Ames decided to be a lawyer again in 1796, but he stayed in politics until he died in Dedham on July 4, 1808.