Murray, who was crowned the greatest player in world tennis, beat Federer in the semi-finals to win his third Olympic title.
He became the first Indian to win three major titles in a row, joining Novak Djokovic, Federer and Stan Wawrinka.
He also became the youngest player to win two Olympic gold medals, joining Nadal, Rafael Nadal and Andy Murray.
He was also the first American to win the men’s singles title at the Olympic Games.
Murray’s victory was marred by a broken serve as he went down 4-2 6-3 6-5 6-2 in the third set of the quarter-finals.
Federer and Murray are expected to meet in the semifinals of the final.
Murray said he had no regrets about playing Federer.
“I had a great tournament,” Murray said.
“I have to give all credit to Roger for what he did for me and for my game.
I knew it was going to be a tough tournament for me.
Murray said the tennis world has had its ups and downs.”
The only thing I have to thank him for is that he taught me to play tennis.”
Murray said the tennis world has had its ups and downs.
He said he feels like he has won all the titles he has had.
“For me, this is all a dream come true,” Murray told reporters.
“But for me, it’s a dream that I don’t want to stop.
I want to stay in the sport.”
The British Open is the third time Federer has won the title in three years.
Murray and Federer have been the best players in the world since the opening of the ATP in 1995.
Murray became the highest-ranked man in world sport with a record of 32-3.