Murray was twice pegged back in a punishing battle with the Swiss star but came through to beat Federer for the first time in a Grand Slam 6-4 6-7(4) 6-3 6-7(2) 6-2.
The Scot will now face Novak Djokovic on Sunday in a rematch of last year's final and admits that he expects to be pushed to the limit by the defending champion.
"I didn't see much of Djokovic's semi-final but I heard he played extremely well," he said. "This is his third final in a row here and so he plays great here and I will have to play my best to win.
"I am sure if I get myself in a position to win it it may be easier than it was at Wimbledon for example.
"Every time we play each other it is a physical match, he is an unbelievable mover so I will need to be ready for the pain, but I hope it is a painful match because that means it will be a good one."
Murray is attempting to become the first player in the Open era to win his first two Grand Slams back-to-back when he meets Djokovic in a major final for the third time.