Andy Murray will become the oldest first-time world No.1 since Australian John Newcombe at age 30 in 1974 when the rankings are updated on Monday.
The 29-year-old Briton will take over from Novak Djokovic at the top of the rankings after his Paris Masters semi-final opponent Milos Raonic pulled out through injury on Saturday.
"Yesterday at I believe 4-2 in the first set I started feeling some pain in my leg," fourth-seeded Canadian Raonic told a news conference, referring to his match with Frenchman Jo-Wilfried Tsonga.
"I didn't think too much of it at that point. I had an MRI half an hour ago...they found that I have a grade one tear in the right quadriceps."
Murray was guaranteed to climb from second to first in the rankings if he reached the final.
Serb Djokovic, who has been No.1 since July 2014, was knocked out in the quarter-finals by ninth seed Marin Cilic on Friday.
The Croat was then beaten 6-4 6-3 in the semi-finals on Saturday by American John Isner.
Murray will become the first Briton to hold the top spot, no matter the result of Sunday's final, and the 26th player to reach No.1 since the rankings started in 1973.
Reaching the summit has been a long process for Murray, who has spent 76 weeks at No.2, a position he reached for the first time in 2009.
A turning point in the Scot's career came when he hired Ivan Lendl as a coach in 2011.
During their first stint together, Lendl managed to turn Murray from a four-time Grand Slam runner-up into a two-time major champion. Murray won Olympic gold in London in 2012 and the US Open title later the same year. In 2013, he became the first British man to triumph at Wimbledon in 77 years.
Before winning the US Open, Murray was 0-4 in grand slam finals.
Only one other man in the Open era, which began in 1968, lost his first four major titles matches - Lendl. The Czech-born baseline player then went on to win eight grand slam singles titles during a 17-year career, spending 270 weeks at No.1.
Murray replaced Lendl with Amelie Mauresmo in 2014. Though the Frenchwoman helped him climb back up the rankings following back surgery, the partnership ended in May this year without any new major title.
The Scot reunited with Lendl before Wimbledon, a week after Murray lost to Djokovic in the French Open final.
The move paid off immediately as Murray claimed a second title at the All England Club and a second gold medal at the Rio Olympics. Last week in Vienna he won the Erste Bank Open for his third straight title and has a 45-3 match record since the French Open. Djokovic held the top spot for 122 consecutive weeks.
But after winning the French Open for the first time in June, his form has taken a dip. He lost in the third round at Wimbledon, and in the first round of the Olympics. At the US Open, he won the first set in the final but Stan Wawrinka rallied to beat him.
"He's definitely a player who deserves that," Djokovic said about Murray on Friday. "Undoubtedly, much respect for what he has done. We have known each other since very, very early days. We were, I think, 11 years old when we first played against each other.
And to see how he has raised his level in the last 12 months is quite extraordinary." One person was quick to congratulate Murray on Saturday - his mother Judy.
"You've come a long way baby," Judy Murray tweeted , with an old photo of the two of them on a tennis court.