Federer, who defeated Murray at SW19 to claim his seventh title, booked his place in the showpiece with a remarkable 3-6 7-6 (7/5) 19-17 victory over Juan Martin Del Potro.
The semi-final match lasted four hours and 26 minutes, surpassing Rafael Nadal's victory over Novak Djokovic at the Madrid Masters in 2009 as the longest three-set men's singles match in the Open era.
Federer, who won gold in the men's Doubles with Stanislas Wawrinka in 2008, is now guaranteed at least a silver medal, while Del Potro must recover to battle for bronze on Sunday after leaving Centre Court in tears.
Murray progressed after a brilliant 7-5 7-5 victory over Djokovic in the second semi-final.
The Great Britain player, who has never beaten Djokovic at a grand slam, has managed to take the momentum from his great Wimbledon run into the Games and looked particularly impressive in yesterday's victory over Nicolas Almagro.
Djokovic presented a big step up, of course, but Murray came out supremely aggressive and deservedly went through to a showdown with Swiss star Federer.
There was another epic match in the men's Doubles semi-finals as French pair Michael Llodra and Jo-Wilfried Tsonga defeated David Ferrer and Feliciano Lopez 6-3 4-6 18-16.
In the final, the French duo will face top seeds Bob and Mike Bryan from the USA, who saw off another French pair, Julien Benneteau and Richard Gasquet, 6-4 6-4.
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