Murray is the first British male since 1908 to triumph in the competition following a stunning straight-sets victory on Centre Court.
The 25-year-old breezed through the opening set in just 38 minutes as two breaks of serve saw him take it 6-2.
Murray broke early in the second to go 2-0 ahead before the two players were involved in a marathon third game on the Scot's serve.
Switzerland's Federer was unable to convert five break points as Murray dug deep to hold a game which lasted 20 minutes.
The Wimbledon champion finally got his first game of the set on the board to make it 1-5 before Murray closed it out 6-1, much to the delight of the home crowd.
Both men held for the opening four games of the third, but Murray took control when he seized a break point following an attritional baseline rally between the pair.
The Scot then failed to take two more break points, but it mattered little as he capped a famous afternoon by serving out the match 6-4.