The seven-time Wimbledon champion put in a spectacular performance to defeat the British No 1 7-5 7-5 6-4 and is now looking forward to taking on Novak Djokovic.
Federer will take on the top seed and defending champion Djokovic in the final on Sunday after the world No 1 outclassed Richard Gasquet 7-6 6-4 6-4.
The 33-year-old will be playing in his 10th Wimbledon final and 26th at all the Grand Slams where victory will give him a record eighth All England Club crown and 18th major.
He will now take on the Serb as they??meet for the 40th time on Sunday in a Wimbledon final rematch of last year with??Federer holding a 20-19 winning record over his opponent but they are 6-6 in the majors.
They have met twice at Wimbledon with Federer winning a semi-final in 2012 on his way to his most recent major triumph and Djokovic gaining revenge in last year’s final.
Federer insists he is looking forward to taking on his old foe once more, saying: “Novak’s been the best player for a few years now and has made it difficult for players to win big tournaments.
“We’ve both been there before. I hope I can get this one on Sunday.”
Overcoming his semi-final match up against Murray was not an easy task for the 17-time Grand Slam champion, who admitted having to keep his focus in the heat of a passionate Centre Court.
“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.
“My serve was the key. I’ve been serving very well in this tournament.”
A thrilling 10th game in the second set eventually went Murray’s way, as he faced up to a host of set points and defended each one, before dropping serve in the 12th game.
“I was screaming inside of myself,” said Federer. “Those were set points as??well – 5-4, love-40.
“I thought I didn’t play badly under those circumstances. Andy was able to??elevate his game because I was playing at my very best.
“That was huge for him but still I was able to make the difference right??after.
“I kept the pressure up and then pounced when the chance was there,” said Federer who is a seven-time champion at The Championships.
“Andy’s been playing very well for the season and there’s so much expectation riding on the match that you try to focus and keep it up.
“I played so well on the biggest occasion today and that’s why I got it.”
His victory over Murray was his most impressive performance in recent years and featured 20 aces, 56 winners and just 11 unforced errors.
Deliberating over where he won it, Federer added: “I think on my serve again. I’ve been serving very well for the entire tournament.
“I kept the pressure up, I went for my shots. I kept pushing forwards, stayed focused and it all worked out very well.”
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