The world No. 4's 6-3, 6-4, 3-6, 7-5 triumph consigned a miserable run of 11 semifinal failures by British men to the history books and emulated the achievement of Bunny Austin, the last home challenger to reach the Wimbledon men's final back in 1938.
The 25-year-old had lost at the semifinal stage for the last three years, joining Tim Henman, Roger Taylor and Mike Sangster on the list of British near-misses at the All England Club.
But decades of anguish faded from view in front of a jubilant Centre Court crowd as Murray booked a showdown with six-time champion Roger Federer in Sunday's final.
While Murray's victory has put one ghost to rest, the Scot won't be truly satisfied until he has become the first British man to win Wimbledon since Fred Perry in 1936.
Murray's meeting with Federer will be the Scot's fourth attempt to win a Grand Slam final following defeats at the Australian Open in 2010 and 2011 and the 2008 US Open.
"It's tough to explain [how it feels]. It's a bit of relief and excitement," said Murray who appeared close to tears as he celebrated on court.
"I started the match really well but one loose game let him back in. It was so close in the last two sets … He was hitting some unbelievable winners and had break points at 4-4, but I managed to hang tough there and win it … I tried to stay calm, but it's not easy. There's a lot of pressure and stress but you need to just focus on the next point and not think about what happened in the past … It was an emotional end to the match. I've just got to keep it together for the final. It will be one of the biggest matches of my life."
Tsonga believes Murray may struggle to recover physically in time for the final.
"Andy looked pretty tired at the end and it'll be tough to recover against Roger, but I hope he does," said the Frenchman.
"I am proud of what I have done here. I fought but I lost. Hopefully, I can do better next time."
After surviving a gruelling examination against David Ferrer in the last eight, Murray was battle-hardened and playing with the kind of focused determination he has lacked in the past.
Even so the weight of expectation on Murray could have proved crippling. Yet he showed nerves of steel to emerge victorious from two hours and 47 minutes of high drama.
Murray, who had won five of his six meetings with Tsonga, has often been criticised for his grumpy on-court demeanour but he looked totally at ease as he broke Tsonga in his first service game.
When Tsonga, a beaten semifinalist at Wimbledon last year, earned two break points midway through the set, Murray simply came up with a series of dazzling winners to get out of trouble.
Tsonga had lost just four of his 90 service games en route to the last four, but Murray broke again for a 3-2 lead in the second set when the Frenchman blazed a forehand wide.
Murray easily closed out the second set but, with the finish line in sight, his concentration wavered and Tsonga broke for the first time in the second game of the third set.
Tsonga seized the lifeline and saved three break points at 3-1. He followed that by recovering his composure to close out the set after suffering a painful blow when Murray drove a volley straight into his groin area.
Murray looked back in control when he broke for a 3-1 lead in the fourth set, but Tsonga was going for his shots with abandon and broke straight back with a barrage of sublime winners.
Both players were living on the edge now, saving a pair of break points each, before the match reached an incredible conclusion when Murray unleashed a superb return on match point that was only called a winner once the Scot challenged successfully.
In the build-up to Wimbledon, Murray spent time sitting on the deserted Centre Court thinking back to those painful semifinal defeats and trying to visualise how it would feel to finally win one. Now he knows. – AFP