The match came twenty eight days after the Scot fell to Federer in his first Wimbledon final but history was not to repeat itself as Murray never allowed Federer into the match.
It was the second gold medal for Great Britain yesterday as Ben Ainslie had picked up his fourth Olympic gold medal earlier in the day.
Murray came flying out of the blocks as he dominated the game and it was an error strewn performance from Federer from the very start.
Murray made the breakthrough in the sixth game of the match to open up a 5-2 lead and he was well and truly in control.
He did take the opening set in the Wimbledon final before Federer roared back to take the title but the fight back from the world number one never came.
He broke Federer immediately in the opening set to lead 2-0 but his own serve came under fire in the next game as he was forced to save six break points.
And he saved them all to extend his lead further to 3-0 and Murray was comfortably on his way to the second set.
That proved to be the case as Federer never looked like he was going to get back into the set.
Into the third and the crowd were getting more and more excited about what Murray was on the verge of achieving but he still had one more set to get under his belt before he could celebrate.
The decisive break came in the fifth game of the third set and Federer never got the set back on level terms.
Murray finished the match on an ace to claim the gold medal with a fantastic 6-2 6-1 6-4 victory.
Speaking to Sue Barker on court after the match Murray said: "It's number one for me - the biggest win of my life.
"I have had a lot of tough losses in my career and this is the best way to come back from the Wimbledon final."
Roger Federer picked up the silver medal, the individual Olympic gold medal is the one honour that still eludes him, while Juan martin Del Potro beat Novak Djokovic in the bronze medal match.
FemaleFirst Helen Earnshaw