Federer took the match 6-3, 6-4, 7-6 (13-11)
The match was decided after a see-saw tiebreaker where Federer and Murray held multiple championship and set points respectively.
Murray made a nervous start, dropping his opening service game to go 2-0 behind in the first set after Federer held his first serve then sealed the break with a stunning forehand winner down the line.
In photos: Men's singles final
The Scotsman immediately broke back after chasing down a drop shot from Federer then whipping a forehand past the world number one.
The next four games all went with serve as the pair captivated the Rod Laver Arena crowd with some absorbing rallies, before Federer broke again for a 5-3 lead with another forehand winner.
The top seed then served out the first set to claim the early advantage after 43 minutes.
For the second set Murray swapped his blue shirt for a traditional white one but the colour change did not help his luck as Federer started to dominate.
The set was decided by a single break, in the third game, as the Swiss broke Murray's serve to love with errors starting to creep into the Scotsman's game.
Under pressure to hold his serve, Murray bravely held his remaining games but so did Federer.
He set up three set points with a booming ace, his seventh of the match, then wrapped it up in 46 minutes with a volley.
Murray then held a 5-2 lead and served for the set before Federer broke him and took the match to it's climactic nail-biting tiebreaker.
Yup , just finished watching it on our new LCD HDTV and gosh it was exciting !!!!!!! Congrats to Roger Federer!!! He deserves it!!!