Ivanovic is the 17th woman, and first representing Serbia, to be No. 1.
She entered the French Open at a career-high No. 2, but overtook Sharapova, who lost in the fourth round.
"Being No. 1 now holds more pressure,'' Ivanovic said after beating Dinara Safina in straight sets in Saturday's championship match. "But you're also a professional athlete, and if you want to achieve your goals, you have to learn how to handle the pressure.''
Safina rose from No. 14 to No. 9, matching her career-best ranking.
Sharapova is now No. 2, followed by the losing semifinalists at Roland Garros, No. 3 Jelena Jankovic and No. 4 Svetlana Kuznetsova. Jankovic would have risen to No. 1 if she had beaten Ivanovic in their semifinal.
Elena Dementieva rose from No. 8 to No. 5. Serena Williams slipped one spot to No. 6, and Venus Williams stayed at No. 7. Both Williams sisters lost in the third round at Roland Garros.
There was no change in any of the top six spots in the ATP rankings, with French Open champion Rafael Nadal staying at No. 2 for the 151st consecutive week. The man he beat 6-1, 6-3, 6-0 in Sunday's championship match, Roger Federer, remains at No. 1, extending his record by sitting atop the rankings for the 228th consecutive week.
Novak Djokovic, the Australian Open champion who lost to Nadal in the French Open semifinals, is still No. 3, followed by Nikolay Davydenko, David Ferrer and No. 6 Andy Roddick.
James Blake moved up one spot to No. 7, with David Nalbandian falling to No. 8. Stanislas Wawrinka and Richard Gasquet round out the top 10.
Vieira has no desire to leave
The official fairplay rankings
Notebook: Sharapova to relinquish No. 1 ranking
