Emerson, P Augustus, R Wilson, K Prasath and J Langlet, who haven't seen their families for three years, were first flown to Delhi before they could fly home.
Their families, waiting on Thursday morning at the airport in Tiruchirapalli where the men were to arrive originally, left disappointed after learning that they were taken to Delhi first.
At the Chennai airport, two groups of supporters lined up late on Thursday night. Workers of the BJP were seen holding up posters and banners of Prime Minister Narendra Modi and the party's Tamil Nadu leaders. The rival group comprised members of the state's ruling AIADMK.
The Chennai police did not allow the fishermen to speak to the media.
The AIADMK has accused the BJP of trying to credit its government at the Centre for the fishermen's freedom to make inroads ahead of the 2016 polls in Tamil Nadu, where the party won a single seat in the May national election.
Asked whether his party viewed the fishermen's release as a diplomatic victory that would boost the BJP in Tamil Nadu, Union Minister Pon Radhakrishnan said, "It is not the BJP's victory, it is a victory of our government, our Prime Minister. We don't look at any politics on this."
The five men were sentenced to death last month by a court in Colombo after being held guilty of smuggling drugs into the country. They were arrested in 2011.
Their sentence was commuted by Sri Lankan President Mahinda Rajapaksa on Wednesday.
The Indian government had challenged the conviction in Sri Lanka's Supreme Court and over the weekend, PM Modi had spoken to President Rajapaksa on the phone.
Their sentencing had led to large protests in Tamil Nadu, which says its fishermen are unfairly targeted and arrested by the Lankan navy.
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