Federer was superb on Centre Court, holding serve easily in almost every game and breaking Murray at the end of each set. With the victory, the second-seeded Swiss improved his record in Wimbledon semifinals to 10-0.
On Sunday, Federer will face Djokovic in the final with title No. 8 on the line. Djokovic, a two-time Wimbledon champion, beat Federer in five sets in last year's final.
Djokovic overcame an early barrage of single-handed backhand winners from Gasquet, produced big serves at crucial times and pulled away to win 7-6 (2), 6-4, 6-4 on Friday in sunny conditions on Centre Court at the All England Club.
Djokovic was twice treated by a trainer on his left shoulder near the end of the second set, but showed no sign of injury as he dominated the third set to reach his 17th Grand Slam final.
Djokovic, playing in his sixth consecutive Wimbledon semifinal and seventh overall, extended his dominance over the 29-year-old Gasquet to 12-1. He has dropped just one set to the Frenchman in their last 10 meetings — none in their three Grand Slam matches.
Gasquet, who also reached the semifinals in 2007, had been trying to become the first Frenchman to reach the Wimbledon final in the Open era. Cedric Pioline finished runner-up in 1997. Instead, he wound up losing his 15th straight match to a No. 1-ranked player.
In the day's second semifinal, seven-time champion Federer was up against 2013 winner Murray, in the 24th career match between the two.
Federer has never lost a Wimbledon semifinal and is bidding to reach his 10th final. It's their first matchup at the All England Club since 2012 — when Federer defeated Murray in the Wimbledon final. Murray, however, beat Federer in straight sets the Olympic final on the same court a few weeks later.
Saturday's women's final will pit five-time champion Serena Williams against 21-year-old Spaniard Garbine Muguruza, playing in her first Grand Slam championship match.
Williams will be bidding for her fourth straight major championship, which would complete a “Serena Slam” — a feat she last accomplished in 2002-03. A win would also take Williams three-fourths of the way to a calendar-year Grand Slam, a sweep of all four majors in the same year. Steffi Graf was the last to do that, in 1988.