Wrestling has been reinstated as an Olympic sport for the 2020 and 2024 Games after being dropped from the programme earlier this year.
The sport had to beat bids from squash and baseball/softball to win a vote by the International Olympic Committee members.
Wrestling was dropped from the programme by the IOC's executive board in February and immediately embarked on a major reform programme.
Nenad Lalovic, the Serbian who took over as president of the international wrestling federation in February, said: "We made mistakes but we decided to listen and learn and those mistakes will not happen again.
"We have modernised our federation, our constitution has become much more democratic with more women and athletes in the administration and with the referees absolutely independent."
Wrestling won in the first round of voting with 49 votes, but there was disappointment for squash which finish third with 22 votes, two behind baseball/softball.
The result came as no surprise - the initial exclusion of wrestling has caused uproar in countries such as Russia and the United States, and it is so popular in Japan it would have been unthinkable not to have it as part of the 2020 Games in Tokyo.
Laura Massaro, the British world number two squash player, said she hope the sport would continue to campaign for Olympics inclusion.
She said: "It is really disappointing news to hear that squash has again failed in its bid to make the 2020 Olympic Games.
"Everyone involved in the sport is extremely upset that we won't be part of the games in 2020. We will carry on learning from the bid process in the hope we can make Olympic status one day in the future."
World Squash Federation (WSF) president N Ramachandran admitted that he was grief-stricken at the decision.
He said: "This decision is heart-breaking for the millions of squash players around the world, particularly given the 10-year journey we have been on to join the Olympic Games Sports Programme.
"As the only new Olympic sport on today's shortlist, we believed squash offered something for the future and I still hope that our inclusion may still be possible.
"The feedback we have received from many IOC members for our campaign and our presentation has been very positive and I am encouraged by the vote we received today.
"We have much to offer the Olympic Movement and I am hopeful that today is not the end of our Olympic journey."