The British number one saw off Frenchman Jo-Wilfried Tsonga in an epic battle to reach Sunday’s showdown, where he will face Roger Federer.
In a dramatic moment, Murray challenged the final point which was called out, and was found to be right, taking the fourth set to win the match.
Centre court roared while crowds of fans on Murray Mount broke into screams and cheers as the 25-year-old made history.
A visibly emotional Murray hugged Tsonga after the match. After his trademark "fingers-in-the-air" gesture, the tearful Scot paused, looking at the sky.
Murray will now face six-time champion Roger Federer in the final. The Swiss star beat world number one Novak Djokovic 6-3 3-6 6-4 6-3 earlier today, meaning he has reached a record eight Wimbledon finals.
Murray's friends and family, including mother Judy Murray and girlfriend Kim Sears, could be seen celebrating as the 25-year-old powered to victory.
Afterwards, Murray said his emotions were "tough to explain", saying: "I'm so happy to be through."
Of the dramatic final point, he said: "I thought it was in, I knew when it left my racket it was good."
He said Tsonga told him at the net that he thought it was wide: "He just said, 'well done'."
The Scot spoke of the pressure, saying: "There's a lot of pressure, when you're on the court there's a lot of stress but you have to just try and focus on the next point, not what's happened in the past."
Asked about the pressure on his family, he added: "I'm not really that bothered, it's a lot harder for me that's for sure. It's been a great tournament so far, it's obviously unbelievable having them around and hopefully I can go one better on Sunday."
He again refused to explain why he points to the sky after a victory, but said it was an extremely emotional moment. "It will be one of the biggest matches of my life," he added.
First Minister Alex Salmond said: "Congratulations to Andy on reaching the final, which is a fantastic achievement. He has played brilliantly right through the tournament and given the whole country a lift with his performances.
"The whole of Scotland will be right behind Andy on Sunday, and I'll be there in person to help cheer him on."
Prime Minister David Cameron also congratulated Murray on his victory.
"It is great news that we have our first home-grown men's finalist at Wimbledon for over 70 years, especially in this exciting Olympics year when the eyes of the world are on the UK.
"I'll be watching the final on Sunday and, like the rest of the country, will be getting right behind Andy Murray - I wish him the best of luck."
Number 10 will fly the Saltire alongside the Union Flag on Sunday in support of the Scot.