The Swiss player won 4-6, 7-5, 6-3, 6-4 on Centre Court to earn his first Grand Slam tennis title since the 2010 Australian Open.
Federer, who turns 31 next month, will regain the top ranking in the sport which he last held in 2010.
Murray has now lost all four of his Grand Slam finals. Britain’s 76-year wait for a male Wimbledon champion will be extended by at least another year.
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