The International Olympic Committee (IOC) suspended the IOA on Tuesday for allowing government interference in the election and said the body was no longer entitled to conduct the poll.
Defiant Indian officials went ahead with the election and named Lalit Bhanot as the new secretary-general of the national governing body after his rivals had pulled out.
Bhanot spent 11 months in custody last year following corruption charges that plagued the 2010 Commonwealth Games in Delhi and is out on bail.
The IOA had been directed by a Delhi court to hold the election under a controversial government sports code, while the IOC wanted it to follow its own constitution and the Olympic charter.
Boxing federation chief Abhay Singh Chautala, who was elected unopposed as IOA president, said the court order left them with no other option but to conduct the poll.
"I want to reiterate that we have done nothing wrong by going ahead with the polls. We have to obey the law of the land," Chautala told reporters.
Bhanot said he would quit his post if found guilty in the corruption case.
The IOC has dismissed the election outcome.
"Those elections are null and void, they won't count," IOC spokesman Mark Adams had told reporters. "They can go ahead with them but they won't have any validity.
"We have to regain our confidence that the Indian Olympic Association is acting independently of government and that the government is not interfering. At the moment, the IOC is not satisfied that this is the case."
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