The Swiss master, returning from the longest injury break of his career, capped a resurgent fortnight with a five-set victory over his long-time rival Rafael Nadal which extended his record haul of major singles titles.
His latest Grand Slam win was perhaps his most surprising, as Federer last won a big title at Wimbledon in 2012 and at 35, his best days were considered over.
But Federer beat Nadal 6-4, 3-6, 6-1, 3-6, 6-3 to become the second oldest major-winner in the post-1968 Open era, after Australia's Ken Rosewall won the 1972 US Open aged 37.
The victory made Federer the first man in history to win five or more titles at three different Grand Slam events: five in Melbourne, seven at Wimbledon and five at the US Open.
His fifth Australian Open triumph was thought improbable in the current era ruled by Murray and Novak Djokovic, before the top seeds' early exits opened the door to the title.
Federer, who spent a record 302 weeks at number one and was inside the top 10 from 2002 until 2015, saw his ranking slide to 17 -- his lowest since 2001 -- after he spent six months out last year with a knee injury.
Federer had had surgery for the first time in his career on his left knee in February and after the Wimbledon setback he did not finish the season, missing the US Open and the Rio Olympics.
But he said the long period of rest fuelled his incredible charge at the Australian Open, where he overcame three top-10 players in Tomas Berdych, Kei Nishikori and Stan Wawrinka to reach a record 28th Grand Slam final.
He holds the all-time men's record of 314 Grand Slam wins, and has career earnings of more than US$100 million.
It was also his 89th singles title victory, the third most in the Open era behind Jimmy Connors on 109 and Ivan Lendl's 94.
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