Murray was consumed with a mixture of relief and raw feeling after seeing a ball from a forehand return hit the line to break Tsonga in the 12th game of a brutal fourth set having brought up two break points.
"It was such a close match in the end, both of us had chances," said Murray.
"I started well, had one loose game on my serve at the beginning of the third set and he came back into it.
"It was tough to lose that set - I tried to stay calm but it's not easy. There's a lot of pressure when you're on the court, but you've just got to focus.
"I did well to hang in because he started to play really well."
The ball was initially called out, but Murray challenged the call and replays showed the ball was in to the delight of thousands of British fans on Centre Court and those watching on the large screens outside the showpiece court.
The Scot - 25 from Dunblane in Perthshire - will attempt to become the first British winner of the tournament since Fred Perry in 1936. He will chase his first Grand Slam title against the 16-times Grand Slam winner Roger Federer, who was mightily impressive in defeating defending champion Novak Djokovic in four sets earlier in the day.
Bunny Austin was the last British man to reach a Wimbledon final in 1938, but Murray will have to steel himself emotionally and mentally for the occasion after almost breaking down when he realised the magnitude of what he had just achieved.
He again pointed to the heavens as he has done over the past few weeks in victory, but may need more than divine intervention to unsettle Federer, a man bidding for a seventh Wimbledon title - the total American Pete Sampras declared on - in his eighth final at the event and a return to the world number one ranking at the age of 30.
Murray has appeared in three Grand Slam finals. He lost to Federer in the 2008 US Open and the 2010 Australian Open with Djokovic overcoming him in last year's Australian Open final. He has yet to win a set in a Grand Slam final.
There have been 11 attempts in 74 years to reach the final by British players, but all have come up short. Having lost to Andy Roddick and Rafael Nadal twice in the last four since 2009, Murray was a warm favourite to account for the world number six who had reached the Australian Open final in 2008 as an unseeded player.
He carried a 5-1 lead over Tsonga into the match from their previous meetings, and looked on course for a routine passage to the final as he wrapped up the opening two sets in one hour and 10 minutes.
He recovered from trailing 30-0 in the second game of the first set to make the decisive break with a couple of intelligent groundstrokes.
Tsonga had two break points in the fifth game of the day to break back, but Murray held himself together wonderfully well to stave off the threat aided by a couple of aces late in the game. He oversaw a collection of nine aces in the match.
With Murray encountering few problems on serve and Tsonga appearing tight and sluggish, Murray moved further ahead when he broke for a 3-2 lead in the second set with his opponent's game apparently in some sort of disarray.
By the time it reached 5-3, Murray had won 15 straight points on serve with Tsonga claiming a pitiful 10 per cent of points on second serve.
Tsonga apparently departed the scene for some treatment to a back problem at the outset of the third set. His disappearance seemed to affect Murray, who threw in a slipshod service game in being broken to love to trail 2-0.
It would be a lapse in concentration that would cost him the set with both men failing to break again at 3-0 and 3-1. Tsonga would eventually quell Murray resistance by serving out the set despite falling 30-15 behind after Murray smashed the ball between his legs in the ninth game.
With the tension palpable, the Centre Court onlookers remained mysteriously subdued. Tsonga had suddenly awoken from his slumber with the pace of his forehand from deep suddenly threatening to undermine Murray.
Murray seemed on the right track when he applied the dagger to break for a 3-1 lead in the fourth set only to watch Tsonga respond as a delightful half volley and crushing return forced the set back on serve.
An incredible Tsonga drive down the line saw Murray dive and nudge the ball out of play after he had been lobbed as two break points eluded Murray, who would do likewise in the ninth game to deny Tsonga the chance to serve for the set with a 5-4 lead.
The match seemed destined for a tie-break with wrong calls by the umpire, double faults and challenges only adding to the tension until Murray forced Tsonga to dump a volley into the net to lead 6-5 and 40-15. Seconds later, he was into the final.