Murray's victory over Tomas Berdych in the quarter-final left the Brit just one win away from usurping long-time number one Novak Djokovic after the Serb fell to a surprise defeat at the hands of Marin Cilic on Friday.
Murray becomes only the 26th man to sit top of the pile since computer rankings were introduced in 1973, and the second-oldest debutant in the position after the 30-year-old John Newcombe scaled the heights in 1974.
The 29-year-old also sets a new record for the longest time between becoming number two in the world and number one, having first reached second in the standings back in 2009.
Murray ends Djokovic's 28-month reign as the best in the world to cap off a remarkable year that has seen him claim seven titles, including a second Wimbledon crown and Olympic gold medal.
The three-time Grand Slam winner also becomes the first Brit to be classed as world number one since Fred Perry more than 70 years ago.
The Scot could add his eighth title of the season when he takes on John Isner in the Paris Masters final tomorrow.