Amar is a summa cum laude graduate of Yale College (B.A., 1980) and the Yale Law School (J.D. 1984) and was an editor of the Yale Law Journal. Amar clerked for now-U.S. Supreme Court Justice Stephen Breyer when he was a judge on the First Circuit Court of Appeals.

Amar is the author of numerous publications and books, most recently the acclaimed “America’s Constitution: A Biography.” The Supreme Court has cited his work in over 20 cases, including the landmark 1998 decision in Clinton v. City of New York, which ruled the presidential line-item veto unconstitutional.In their book For the People: What the Constitution Really Says About Your Rights, Amar and Alan Hirsch introduce a variation on the four boxes of liberty theme often quoted by conservatives opposed to gun control. Discussing the American Constitution, they assert that the ideal of citizenship generates four "boxes" of rights. The first three are the ballot box, jury box and cartridge box. To these, with some reservations, they add the lunch box: the idea of a social safety net that supports basic physical and educational needs.

He was a consultant to the television show The West Wing, on which the character Josh Lyman refers to him in an episode in Season Five. His course on constitutional law is one of the most popular undergraduate offerings at Yale College. Amar's younger brother, Vikram Amar, teaches at the UC Davis School of Law.

Amar is currently a Visiting Professor of Law at Pepperdine School of Law and was also named the B.R. Ambedkar Professor of Indian Constitutional Law at Columbia Law School in April 2010. He has also lectured for One Day University. He was a Visiting Professor of Law at Suffolk University Law School during the Fall 2006 semester.

In 2008, Presidential candidate Mike Gravel said that he would name Amar to the Supreme Court if elected President.

Amar graduated from Las Lomas High School in Walnut Creek, California in 1976.