Federer, 33, will be playing in his 10th Wimbledon final on Sunday and 26th at all the Grand Slams where victory will give him an eighth All England Club crown and 18th major.
His demolition of 2013 champion Murray was his most impressive in recent years and featured 20 aces, 56 winners and just 11 unforced errors.
He allowed Murray, who he has now defeated in five out of six Grand Slam clashes, just one break point and that was in the opening game of the two hour seven minute match.
"It's been tough, Andy has been playing very well this season and there was so much expectation on this match," said Federer, who is the oldest finalist since 39-year-old Ken Rosewall in 1974.
"I had to try to focus and keep holding my serve one more game. You do it so many times you think the break will go against you eventually, but I managed to hold on.
"I was unbelievably happy. I maybe didn't show it at the end because the crowd went quiet. People maybe expected it to go four sets, me as well.
Murray said he had served well and was happy with his performance.
"Roger served fantastic. I had one break point in the first set but after that I didn't get any opportunities," admitted Murray who was looking to make the Wimbledon final for a third time.
"The pressure built and I was broken at the end of all three sets. But I didn't play that badly. I had a good match."ederer fought off a break point in the opening game, but then neither man blinked until the Swiss carved out his first opportunities in the 12th game.
Federer fired 11 aces, 23 winners and committed just three unforced errors.
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