The 33-year-old Swiss became the oldest All England Club finalist since 39-year-old Ken Rosewall in 1974 when he swept past 2013 champion Murray 7-5, 7-5, 6-4 to set up a rematch of last year's final against Novak Djokovic, a clash he lost in five sets.
Victory put Federer into his 10th Wimbledon final and 26th at all the Grand Slams where he will seek a record eighth All England Club title and 18th major. His victory over Murray was his most impressive performance in recent years and featured 20 aces, 56 winners and just 11 unforced errors.
"It's definitely one of the best matches I've played in my career. The first set, I don't remember point by point, but it was definitely really, really solid," said Federer who is now just one win away from becoming the oldest champion at Wimbledon in the Open Era.
"Today I was clearly able to play very well from the start. The beginning was always going to be an important part of the game.
Friday's win also took the seven-time champion's record at the All England Club to 79 wins against just nine defeats.
It is by far his best Grand Slam tournament.
He has five titles at the US Open and a win-loss record of 72-10, four Australian Open victories from a 75-12 run and is 65-16 at the French Open where his lone title came in 2009.
Federer has also now won all 10 semi-finals in which he has appeared at Wimbledon.
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