The Swiss second seed will face Scotland's Andy Murray in what will be his 37th Grand Slam semifinal for a place in Sunday's title match.
Murray, playing his eighth successive Wimbledon quarterfinal, cruised to a 6-4, 7-5, 6-4 win against unseeded Canadian Vasek Pospisil on Wednesday.
After collecting his 150th Grand Slam match victory the 28-year-old Scot will square off against Federer on Friday.
Defending champion and top seed Novak Djokovic eased into the semifinals for a sixth successive year and seventh time in total by demolishing ninth seed and US Open winner Marin Cilic 6-4, 6-4, 6-4.
The world number one, who also won Wimbledon in 2011, goes on to play French 21st seed Richard Gasquet who defeated Switzerland's Stan Wawrinka in a five-set thriller.
Wawrinka, this year's Roland Garros champion, was unable to complete a clean-sweep of the semifinals by the top four as Gasquet stunned the fourth seed 6-4, 4-6, 3-6, 6-4, 11-9 to reach his second Wimbledon semifinal, eight years after his first.
Gasquet fell to the ground after beating the Lausanne native in a game that teeter-tottered through three hours and 28 minutes of play.
Federer, bidding to become the oldest Wimbledon champion in the Open Era, shrugged off two rain delays as well as being broken for the first time at the tournament to complete victory in just 94 minutes.
The 33-year-old Basel native fired 11 aces and 36 winners as he secured a sixth win in eight meetings with Simon, who was attempting to reach the last-four of a major for the first time.
"The stop and go with the rain are always tough but I think I used them to my advantage," said Federer.
"They helped me rather than hindered me."
He said he was looking forward to the prospect of a semifinal against 2013 champion Murray.
Federer defeated the British third seed in the 2012 Wimbledon final before Murray gained revenge just weeks later in the Olympic Games final.
"We both like to look back on that summer of 2012," Federer said.
"If we knew I would win Wimbledon and him Olympics, I think we both would have taken it. It was a great summer for us."
Federer broke for a 3-0 lead in the first set against Simon before rain sent the players off Court One for the first rain delay.
Forty minutes later, they returned and Federer swiftly claimed the opener on the back of 15 winners to Simon's four.
The Swiss was 4-3 up with a break in the second and then moved to 5-3 on his 116th consecutive service hold, a streak stretching back to the first round in Halle last month.
But that record was shattered in the next game when 30-year-old Simon broke the 17-time major winner, who had only faced two break points at this year's Wimbledon before Wednesday.
Federer took swift revenge, however, by regaining the advantage and he was serving for a two sets lead when the showers returned, causing another hold-up for 40 minutes.
It had little effect on the Swiss great as a service winner and back-to-back aces gave him the second set 7-5.
Federer breezed through the decider with breaks in the first and seventh games.