Wrestling won the first round of voting with 49 of the 95 votes cast. The joint bid by baseball/softball, not on the programme since 2008, got 24 votes, while squash, which has never featured in the Olympics, received 22.
Earlier in the day, the IOC approved the 25 core sports at the Summer Games with a 77-16 majority.
Wrestling will now be seen not only in the 2020 Tokyo Games but also in the 2024 Summer Olympics.
It has been a great turnaround of fortunes for wrestling that was dropped in February this year by the 15-member executive board as IOC looked to refresh its sports programme.
It provoked an unprecedented outcry.
Wrestling dates back to the ancient Olympics. Either Greco-Roman or freestyle wrestling or both have been in every modern Olympics, except in 1900.
In May, the same executive board gave wrestling a second chance as it put it on the three sport shortlist to be considered by the entire IOC membership in Buenos Aires.
World body FILA had made extraordinary progress since being provisionally dropped by the IOC, changing its leadership, making the management more democratic and transparent and revising competition rules.
"Thank you for this opportunity of saving our sport," wrestling federation president Nenad Lalovic told the IOC. "This is the most important day in our 3,000-year history. Remaining in the Olympics is crucial for wrestling's survival."
Lalovic, a Serbian, has been leading reforms and was also at the forefront of lobbying since he was installed president after his predecessor was forced to resign in the aftermath of the sport being dropped from Olympics.
"We made mistakes and admitted to them," Lalovic said while answering questions from IOC members after the 20-minute presentation.
Lalovic that it would be a decision the IOC would not regret.
"With this vote, you have shown that the steps we have taken to improve our sport have made a difference. I assure each of you that our modernisation will not stop now. We will continue to strive to be the best partner to the Olympic Movement that we can be.
"To the millions of wrestlers, supporters and fans around the world that came together to save Olympic wrestling; I offer a very big thank you," said Lalovic, whose son represented Serbia at the international level.
He added: "Every one of you fought very hard for this victory."
--IANS (Posted on 09-09-2013)