Murray advanced to the final courtesy of a straight-sets victory over the world number one, who struggled with his serve throughout the match.
However, despite Federer not being on top form, Murray believes that any win against such a legendary player is a memorable one.
"He didn't serve that well for him tonight, so I was able to be very aggressive on his second serve," Murray told the ATP Tour's official website.
"He maybe slowed down his first serve a little bit, so I was able to take a few more chances. Obviously that helped.
"I went for it, like I did the past few times I played against him, and it worked tonight. When you're beating the best player of all time probably, it's obviously going to be special."
Murray will now face world number two Novak Djokovic in tomorrow's final as he looks to win the event for the third consecutive time.