Murray started the contest well but could not stop the 17-time Grand Slam winner from pegging him back and eventually going on to dominate proceedings at the O2 Arena.
Despite Murray playing on home soil it was Federer who seemed to enjoy the backing of the majority of the London crowd and he received a huge ovation after completing the win an hour and 33 minutes.
Federer, who is chasing a seventh title in the season-ending event, will play Novak Djokovic in Monday's final in a clash between the top two players in the world.
Murray's prospects seemed a lot brighter when he made the best possible start by breaking his opponent's serve in the first game and then dictating the play in the opening stages.
The British No 1 was taken to deuce in the sixth game but showed great composure to close out the game with some assertive play at the net.
But Federer finally did get the break back in the eighth game and the set went into a tie-break, where Murray took an early advantage only for the second seed to turn the tables in expert fashion.
Federer then broke again in the third game of the second set, fighting back from 40-0 down to win five straight points as the Swiss player began to take a stranglehold on the contest.
And the hammer blow came in the seventh game of the set as an aggressive Federer went a double break up after firing a brilliant backhand winner past a helpless Murray.
The 31-year-old then comfortably served out the win to stay on course for a third straight title in the event.