Djokovic, the world number one, survived an unusually sloppy start and eventually dismissed the French 21st seed with 12 aces and 46 winners in two hours and 20 minutes on Centre Court.
The 28-year-old will go for his third All England Club title, and his 9th at the majors, when he faces 7-time Wimbledon champion Roger Federer in Sunday's final. Federer beat Andy Murray 7-5, 7-5, 6-4. Djokovic defeated Federer in last year's final and lost to Murray in the 2013 showpiece.
"It was a very good performance considering the occasion. Semi-finals are always tough and things could have gone his way in the first set. That was the turning point," Djokovic said after booking his 17th Grand Slam final berth.
Djokovic played down concerns about a left shoulder injury that twice needed treatment and insisted he would be ready for the final.
"It's nothing that worries me honestly. It will be fine for the next match," he said.
"I have a responsibility to play well here in the cradle of tennis. It is an honour to play in the Wimbledon final - the most watched tennis match in the world.
"I'm just glad to reach another final. I will be ready for it."
Gasquet added: "I did a good match, but the tie-break was important, winning that would have given me confidence.
"It was 2-2 in the tie-break then it was 7-2 very fast. He never missed. That's why he's number one in the world."
For the first time, Djokovic has made the Wimbledon, Australian and French Open finals in the same year. Djokovic, who also won Wimbledon in 2011, now has a remarkable 47-3 record in 2015 and one more win would give the reigning Australian Open champion his second Grand Slam of 2015.
It would also go a long way to erasing the heartache of his French Open final loss against Stan Wawrinka last month - a defeat that denied Djokovic the only major title to elude him.
Blow for blow
Watched by a Royal Box packed with celebrities including Thierry Henry, Alex Ferguson and Bjorn Borg, Djokovic once again showed how tough he is to take down.
Gasquet's surprise run had brought him back to the Wimbledon last four for the first time since 2007. The 29-year-old, who was bidding for a first major final, caused one of the bigger upsets in this year's tournament when he knocked out Wawrinka in quarter-finals.
But Djokovic had won 11 of his 12 previous meetings with Gasquet and, despite the Frenchman's strong showing, the top seed would eventually cruise to victory number 12. He seemed set for another quick-fire win after breaking in the opening game against Gasquet.
Unexpectedly, the Serb lapsed into an error-strewn period that left him visibly frustrated as Gasquet began to take control. Unfurling his majestic one-handed backhand whenever the opportunity arose, Gasquet broke back and matched Djokovic blow for blow all the way to the tie-break.
But the tenacious Serb couldn't be subdued forever and, raising his game at just the right moment, he blitzed Gasquet in the breaker with a series of searing winners. It was rough on Gasquet, but despite making only five unforced errors he found himself a set down.
Djokovic kept the heat on Gasquet at the start of the second set, breaking with a brilliant forehand that curled cross-court past his stranded opponent. Confidence was surging through Djokovic now and he somehow stretched to track down a powerful Gasquet forehand and turn it into an blistering on-the-run winner.
Although Djokovic twice called for treatment on his left shoulder, an injury sustained in a first set tumble, even that impediment couldn't stop him easing to a two-set lead. With another Wimbledon showpiece in sight, Djokovic turned the screw, cleverly moving Gasquet into awkward positions to induce the errors that brought a decisive break in the third game of the third set.