Federer, the six-time champion, needed only 90 minutes to pummel the Russian 26th seed Mikhail Youzhny into submission, taking a 6-1, 6-2, 6-2 victory at Centre Court.
Djokovic, the defending champion and world No 1, also took the express route, against the German 31st seed Florian Mayer, recording an comfortable 6-4, 6-1, 6-4 victory on Court One.
Now Djokovic will attempt to reach his second successive Wimbledon final by extending his current winning streak against Federer to four matches in their first encounter at the All England Club.
Djokovic has dominated the rivalry of late, beating Federer in the semi-finals of the US and French Opens, but the Swiss still holds a 14-12 edge in their 26 career meetings.
"It's always a pleasure playing against Roger. I'm looking forward to it," Djokovic said.
"He is a great champion and has been so dominant and consistent at the grand slams. He is the ultimate challenge on grass courts."
Djokovic has every reason to feel confident, but Federer, who has now reached a record 32 grand slam quarter-finals, looked in peak form as he delivered a command performance in front of Prince William and wife Catherine.
"I played great. Maybe my game matches up well against Mikhail," said Federer, who last won Wimbledon in 2009. "It helps when royalty and other stars come to watch, it's inspiring and a thrill and helps tennis."
Federer, who is without a grand slam title since the 2010 Australian Open, cruised to a 14th win in 14 meetings against Youzhny and, just as importantly for the 30-year-old Swiss, there were no signs of the back pain which had dogged him in the fourth round against Xavier Malisse.
Federer, chasing Pete Sampras's record of seven Wimbledon titles, also put an end to a worrying sequence at the All England Club; he had been knocked out in the quarter-finals in the past two years.
France's Jo-Wilfried Tsonga reached his second successive Wimbledon semi-final with a 7-6, 4-6, 7-6, 6-2 win over the German Philipp Kohlschreiber.
Tsonga, the No 5 seed, danced around Court One in delight after breaking Kohlschreiber for the second time in the fourth set. He sealed victory on his first match point after rushing to the net and firing a cross-court winner, clinching victory after two hours, 48 minutes.
Tsonga told the BBC: "It was difficult. Philipp played well, he served well, he was better than me on the baseline, he was very aggressive.
"But I'm through, and I'm happy. It doesn't matter who I play in the semi-final."
He added: "It's a second chance after last year. I will try to play my best tennis and try to win. I have had a lot of support from the crowd here."
Murray eventually triumphed 6-7, 7-6, 6-4, 7-6.
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