Nadal, the world number two bidding to become just the third man in the Open era to win the French Open and Wimbledon titles in the same year, eased past Tomas Berdych of the Czech Republic 7-6 (7/1), 6-4, 6-2.
The Spaniard, runner-up to Federer in 2006, will play Serbia's Djokovic who needed a marathon five hours to see off 10th seeded Cypriot Marcos Baghdatis 7-6 (7/4), 7-6 (11/9), 6-7 (3/7), 4-6, 7-5.
Federer holds a 5-1 career lead over Gasquet including a straight sets win in the Wimbledon first round last year.
"Richard is a wonderful player off the back of the court," Federer said of his semi-final opponent.
"He mixes it up very well and comes to the net much more. He's got a great slice and a fantastic backhand.
"He's going to be one of the good players of the future."
Biggest grand slam run for Gasquet
Gasquet will be playing in his first grand slam semi-final but faces the prospect of returning to the court to face the world cumber one as early as 1100GMT on Saturday after his own epic five-setter against Roddick.
Richard Gasquet, right, celebrates his big win
as Andy Roddick, left, is dejected [AFP]
"I prefer to play him in the semi-finals for sure than in the first round last year because I was disappointed with my draw," Gasquet said.
"It will be hard for me because I won, so I'm really happy, but I have another match tomorrow. Maybe I will be a little bit tired."
Roddick, runner-up to Federer at Wimbledon in 2004 and 2005, said he was stunned by one of the most painful defeats of his career.
"It's as hard a defeat as I've had to take. I played OK but I thought he played very well.
"It's another missed opportunity at Wimbledon. I'd love to tell you what it feels like in the pit of my stomach but I don't think I'm articulate enough to do that."
Seven-straight for Nadal
Meanwhile Nadal is pressing to become the first Spaniard to win the men's singles title since Manolo Santana in 1966, but would have to play seven days in succession after being badly affected by the constant rain interruptions which have made this Wimbledon the wettest since 1982.
Nadal's five-set match against Robin Soderling stretched over four days, beginning last Saturday and finsihing on Wednesday, after which the French Open champion then came back from losing the first two sets to see off Russia's Mikhail Youzhny in the fourth round.
"I haven't had the best draw," said Nadal.
"But today I played a great match in very difficult windy conditions. I am very happy with my Wimbledon.
"I am in the semi-finals and I have beaten some very good players on grass - Mardy Fish, Soderling, Youzhny, Berdych."
Djokovic the marathon man
While Federer and Nadal were quickly into the semis, 20-year-old Djokovic was involved in another Court One epic after his four-hour match against 2002 champion Lleyton Hewitt in the fourth round on Thursday.
On Friday, Djokovic reached his first Wimbledon semi-final the hard way taking five hours to overcome Baghdatis.
"I don't know how I won that, especially after the last long match," Djokovic said.
"I'm exhausted and emotional. It's unbelievable.
"Those long matches are not really expected on grass. The crowd had something to cheer because we played an incredible match."