Incredible India is the name of the country's tourism campaign.
Khan was the face of the campaign for 10 years, and speculation was rife that he had been removed because of comments he made about intolerance in India.
The authorities denied reports that the actor had been fired; but said that his contract had ended.
"It is the prerogative of the government to decide whether they need a brand ambassador for any campaign, and if so, who that ambassador should be," Khan said in a statement on Thursday.
"Whether I am brand ambassador or not, India will remain Incredible, and that's the way it should be."
The actor had come in for severe criticism after he told a journalism awards ceremony that he was "alarmed" over the rise in acts of intolerance in the "last six to eight months".
Rising protests over the issue of "intolerance" put Indian Prime Minister Narendra Modi's government under pressure when a movement that began with writers returning state awards spread to scientists, historians and filmmakers.
Khan's statement even found its way to parliament when India's home minister made remarks that were seen as a jibe against the Bollywood superstar.
India's tourism ministry has expressly clarified that it had never directly employed Khan, and that his departure as the ambassador for the campaign was incidental.
"Our contract was with the McCann Worldwide agency. The agency had hired Aamir for the job. Now the contract with the agency is over. Ministry has not hired Aamir," Tourism Minister Mahesh Sharma was quoted as saying by the Press Trust of India news agency.
"It was the agency which has hired him. Since the contract with the agency is no more, automatically the arrangement with the actor no longer exists," he added.
Indian actor Aamir Khan has said he respects the government's decision not to renew his contract as the ambassador of its "Incredible India" campaign.