The walkover sees Murray take over from Serbia's Novak Djokovic, who had held the top ranking since July 2014.
The Scot will look to cap his incredible charge to the summit of the game with victory over John Isner in Sunday's final after the American saw off Marin Cilic of Croatia 6-4 6-3 in the first semifinal.
Murray will be bidding for his eighth title of the season, including winning Wimbledon for the second time and Olympic singles gold in Rio.
He is on an 18-match unbeaten run which has swept him past the faltering Djokovic, who held a massive lead after claiming the French Open title in May.
"To get to No. 1 isn't about today, but it's about 12 months of tournaments to get to this stage," Murray told the official ATP Tour website.
"The last few months have been the best of my career and I am very proud to have reached No. 1. It has been a goal of mine for the past few years."
At 29 years of age, Murray is the second oldest player to achieve the status for the first time. Australian legend John Newcombe was 30 when achieved it for the first time back in 1974.
He joins a select group of 26 players to take the No.1 spot since computerized rankings were introduced in 1973 and one of them, Boris Becker, who is now Djokovic's coach, was quick to congratulate him on social media.
Only Raonic stood in his way, but the Canadian suffered a muscle tear in his right leg in beating Jo-Wilfried Tsonga.
"This morning I had trouble waking up and getting out of bed. So I went to sort of clear any serious diagnosis," said Raonic.
Murray will be officially confirmed as the new number one when the latest rankings are released on Monday.
Isner beat Cilic for the first time in seven attempts as he bids for his first Masters 1000 title.
The giant Isner will face an uphill task against Murray, who had spent a total of 76 weeks in the second spot since first reaching that mark in 2009, but is in the form of his life.
He is the first British men's player to top the modern rankings and fittingly will receive the No.1 trophy at the launch of the ATP World Tour Finals in London on November 10.
His brother, Jamie Murray, achieved No.1 in the doubles rankings for the first time earlier this year and the pair have been integral to Britain's success in Davis Cup in recent years.
Mum Judie tweeted with pride after Raonic's unfortunate injury handed Andy the top spot he had coveted for so long.
She was instrumental in spotting and honing the talent of both brothers in their hometown of Dunblane, Andy first wielding a racket at the tender age of three.
When he was eight years old, Murray survived a mass shooting at his school that claimed the lives of 16 children and one teacher after a 43-year-old local man, Thomas Hamilton, went on a deadly rampage before killing himself.
In 2013, Murray became the first British man to win Wimbledon for 77 years, having claimed his first grand slam title at the US Open the year before, shortly after winning the Olympic singles title for the first time in London.
As news of his latest achievement spread, Murray received a message of congratulation from Scotland's first minister Nicola Sturgeon and a host of other sporting stars.
ATP president Chris Kermode also paid tribute to Murray's feat: "Andy has shown incredible dedication, determination and hard work in his bid to get to number one.
"It's difficult to think of a player more deserving of this accolade -- in one of the toughest eras in the history of our sport. "