The 22-year-old Sinner is the first player from Italy to reach No.1 since the computerised rankings began in 1973. He will be the top-seeded man at Wimbledon, where play begins on July 1.
Sinner is 33-3 this season with three titles, including earning his first Grand Slam trophy at the Australian Open in January, part of a 19-0 run to begin 2024.
Two of those three losses were against Carlos Alcaraz. One came on Friday in five sets in a semi-final at the French Open, which Alcaraz went on to win by beating Alexander Zverev in Sunday's final.
Alcaraz's third major title helped him rise one place in the rankings to No.2, with Djokovic third and Zverev remaining at No.4.
Djokovic was the defending champion in Paris and needed to get back to the final in order to stay at No.1 because of his lack of play this year and failure to reach the title match at any tournament so far.
He tore the meniscus in his right knee during a fourth-round victory over Francisco Cerundolo at Roland Garros last week, withdrew before the quarter-finals and underwent surgery.
Iga Swiatek's third consecutive championship at Roland Garros - her fourth there in five years and fifth major title overall - allowed her to increase what already was a large lead atop the WTA rankings.
Swiatek already was so far ahead of everyone else heading into the French Open that she would have held onto the top spot even if she had lost in the first round.
Coco Gauff climbed one spot to a career-high No.2. The 20-year-old American, last year's US Open champion, reached the French Open singles semi-finals before losing to Swiatek.
Two-time Australian Open champion Aryna Sabalenka swapped places with Gauff and went to No.3, followed by 2022 Wimbledon winner Elena Rybakina.
Jasmine Paolini, a 28-year-old Italian who lost to Swiatek on Saturday in her first major final, jumped into the top 10 at a career-best No.7.
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