Murray progressed past fifth seed Jo-Wilfried Tsonga 6-3, 6-4, 3-6, 7-5 to become the first British player in the final since 1938.
Meanwhile, Federer recorded an impressive victory over world number one Novak Djokovic 6-3, 3-6, 6-4, 6-3 to reach the decider as he aims for a 17th career Grand Slam.
“He’s one of the greatest ever players,” Murray saud. “It’s a great challenge, one where I’m probably not expected to win, but one that, if I play well, I’m capable of winning.
“The pressure that I would be feeling if it was against somebody else I guess it would be different. But there will be less on me on Sunday because of who he is.”
Meanwhile, Federer, who hasn’t won a major title since the 2010 Australian Open, told reporters: “There’s a lot on the line for me. I’m not denying that. I have a lot of pressure, as well. I’m looking forward to that. That’s what I work hard for.”