Wawrinka was on a 12-match winning streak at Roland Garros, having overpowered Novak Djokovic in the final 12 months ago, but he had no answer to the brilliance of Murray.
Murray dominated the opening two sets, then weathered a Wawrinka fightback to win 6-4 6-2 4-6 6-2 in two hours and 35 minutes.
The world number two will now attempt to emulate Wawrinka’s achievement from last year when he takes on Djokovic today.
Having followed in the footsteps of Britain’s 1937 runner-up Bunny Austin by winning his first French Open semi-final at the fourth attempt, Murray will hope to once again succeed Fred Perry, the last British man to lift the Coupe des Mousquetaires in 1935.
The 29-year-old raised a fist aloft after hitting the match-winning volley, and said with his voice cracking: “I knew if I was going to win, I was going to have to play one of my best clay-court matches.
“Stan has been unbelievable the last two years. I’ve played one of my best matches today and I’m looking forward to the final. I’m extremely proud. I never expected to reach the final here. I’d always struggled on the clay.”
Murray may have been the higher seed but it was tough to make a case for him being the favourite. Not only was Wawrinka the defending champion, he had also beaten Murray in their last three matches and had never lost a set against him on clay.
Murray, meanwhile, had lost all six of his slam matches against top-four opponents since beating Djokovic to win Wimbledon in 2013.
Novak Djokovic stormed into a sixth consecutive grand slam final with a crushing win over first-time French Open semi-finalist Dominic Thiem.
For the second year in a row, Djokovic will now have the chance to complete his career Grand Slam.
With Djokovic playing in the last four at a slam for the 30th time and Thiem making his debut, the danger was always that it was going to be a blow-out, and so it proved.
The world number one dropped only three games in the opening two sets and then won six of the final seven games to cruise to a 6-2 6-1 6-4 victory.
Only Djokovic has won more matches than 22-year-old Thiem this season, and the consolation for the Austrian is that he will make his top-10 debut next week.
He had played superbly to beat David Goffin in the quarter-finals but could find no way to penetrate Djokovic’s legendary defences.
Meanwhile, Serena Williams hopes her worst grand slam defeat can pave the way for her finally to equal Steffi Graf’s Open era record of 22 titles.
The world number one reached yet another slam final with a 7-6 (9/7) 6-4 victory over Kiki Bertens.
She won her 21st slam singles title at Wimbledon last year but since then has lost to Roberta Vinci in the semi-finals at the US Open and Angelique Kerber in the final of the Australian Open.
Her opponent todaywill be Spain’s Garbine Muguruza, the same player Williams beat in the Wimbledon final 11 months ago.
But Muguruza also handed Williams her heaviest ever loss at a slam at Roland Garros two years ago, beating the great American 6-2 6-2 in the second round.
“I learned so much from that match,” said Williams. “I hate to lose, but when I do, I hope it was worth it.
“That match was definitely one of those that was kind of needed and worth it.”
If she is to beat fourth seed Muguruza this time, Williams will surely have to play better than she has in her last two matches.
After dicing with elimination in her quarter-final against Yulia Putintseva, Williams again was below her best against Bertens, who considered not starting the match because of a calf injury.