The Scot beat Jo-Wilfried Tsonga in four sets to set up a showdown with six-times champion Roger Federer, becoming the first British man to reach the final since Henry “Bunny” Austin.
The Centre Court crowd, including mother Judy Murray and girlfriend Kim Sears, broke into screams and cheers as the 25-year-old sealed his victory.
Afterwards, Murray said his emotions were “tough to explain”, saying: “I’m so happy to be through.”
Prime Minister David Cameron was one of the first to congratulate 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 tomorrow in support of the Scot.
First Minister Alex Salmond said: “The whole of Scotland will be right behind Andy on Sunday, and I’ll be there in person to help cheer him on.”
Among the crowds cheering for Murray on Centre Court were pop star Kylie Minogue with boyfriend Andres Velencoso in the Royal Box, joined by Sir David Frost, Vogue editor Anna Wintour, cricketer Sachin Tendulkar and former Wimbledon champions Goran Ivanisevic and Rod Laver.
The Duke of York was also present, as was Princess Michael of Kent and Lady Annabel Goldsmith, and also Deputy First Minister Nicola Sturgeon.
Meanwhile, in the star’s home town of Dunblane, residents were confident he can lift the trophy after victory over Federer tomorrow.
John Nixon was watching the match at the Dunblane Youth and Sports Centre which was busy with supporters of the British number one.
He said: “I could barely watch, the tension was too much. It’s fantastic, it’s great for Andy, great for Dunblane and great for the country as well.
“He is going to be under enormous pressure in the final but all we can do is hope.
“Federer is playing some amazing tennis but you just get the feeling this year is going to be the year.”
Mr Nixon spoke of Murray as a “great ambassador” for the sport and Dunblane.
“He is a clean living young man, his parents and grandparents are so proud of him.
“I’m just delighted for the whole family.”
Pubs in Dunblane got into the Wimbledon spirit by serving strawberries and cream to
Posters of Murray started to appear across the town alongside signs reading “good luck” and “go Andy”.
Dunblane Centre manager Gemma Grier said: “Everyone in Dunblane is so excited and will be cheering him on in the final.”
Murray hopes to become the first British man to win Wimbledon since Fred Perry 76 years ago.