Federer knocked out defending champion Novak Djokovic 6-3, 3-6, 6-4, 6-3.
The Swiss star will be bidding for his seventh Wimbledon and 17th Grand Slam titles -- and a return to No. 1 in the world rankings.
Murray, 25, became Britain's first male Wimbledon finalist in 74 years with a 6-3, 6-4, 3-6, 7-5 decision over Jo-Wilfried Tsonga of France.
Federer, seeded third, and the fourth-seeded Murray will meet Sunday for the title.
If Federer wins, he'll replace Djokovic as No. 1 in the world.
Federer and the defending champion battled for just under 2 1/2 hours -- playing under the roof on Center Court because of rain.
After swapping sets, Federer took the pivotal the third set with an overhead smash, seized a 2-0 lead in the fourth and won on his first match point when the 25-year-old Serb hit a forehand into the net.
Federer had only 10 unforced errors to 21 for Djokovic and slammed 12 aces.
"I was able to play some fantastic tennis today," Federer said. "I hope I can play a good match on Sunday."
Federer will be appearing in a record 24th Grand Slam final.
Scotland native Murray and Tsonga played on Center Court, with the roof open under sunny skies.
Murray will try to give Britain its first male Wimbledon finalist since 1938 and first winner since Fred Perry took the title in 1936.
After his win over Tsonga, Murray told the BBC he felt "a bit of relief ... excitement."