According to the Australian Open official website, the top-seed's ability to seize on vital opportunities proved to be the difference against the 22-year-old, as he fought off a late challenge to win the match 6-3 6-4 7-6(11) in two hours and 41 minutes before a capacity crowd at Rod Laver Arena on Sunday night.
Murray fought bravely against his more experienced opponent, but lacked the composure that aided Federer on the crucial points to eventually succumb to the Swiss.
The victory marks the fourth time Federer has won the Norman Brookes Challenge Cup at Melbourne Park, his triumph on Sunday adding to victories in 2004, 2006 and 2007.
Federer's win was only his fifth against Murray in 11 matches, but it did mark the second time he had beaten him in a Grand Slam final after a straight-sets win in the 2008 US Open final.
Attempting to become the first British male to win a Grand Slam singles title in 74 years, Murray found himself down a break at 0-2 in the first set before rallying to break back and then level at 2-2.
Federer then saved three further break points to hold serve at 3-2, firing down two aces as the Scot threatened to grab the momentum.
However, it would be the Swiss who made best use of his opportunities in the first set. He produced a superb backhand winner down the line to convert a single break point against Murray's serve in the eighth game to lead 5-3.
The 28-year-old then served out the set, sending down his fourth ace of the match in claiming it 6-3. Although the nine games had been tightly contested, the Scot was able to convert only one of his four break point chances, while Federer jumped on two of his three and hit 12 winners to Murray's five.