Governor Banwarilal Purohit and Chief Minister K Palaniswami greeted people on the occasion.
The lockdown prompted muted celebrations, as people confined themselves to homes to offer prayers indoors.
People greeted each other over phones and through social media platforms, even as temples, generally buzzing during the new year, remained closed due to the lockdown.
Many households prepared special delicacies to enjoy the Tamil new year, the first major festival to be celebrated during the ongoing lockdown.
Incidentally, Prime Minister Narendra Modi on Tuesday announced extension of the national lockdown till May 3 as part of the country's fight against COVID19.
On Monday, Palaniswami had announced that the state was extending the lockdown till April 30.
Extending his greetings, Purohit said the new year is celebrated on the first day of Tamil month 'Chithirai' every year to "mark the onset of peace, prosperity and joy in our families" and stressed on social distancing.
"It (the new year) marks the greatness of our tradition, heritage and culture. May the state and its people be filled with hope and happiness for a glorious future during this year," he said in his message.
Purohit urged people to resolve to work together in the spirit of harmony and friendship to usher in progress and development so as to create a brighter and better tomorrow.
"I also request all the people of Tamil Nadu tofollow the government guidelines regarding COVID-19 scrupulously and to stay at home and be safe," he said.
Palaniswami said the Tamil people, known for their pluralism and culture, had been celebrating the new year in 'Chithirai' for long.
His government was striving to realise the late chief minister J Jayalalithaa's aim of making the state numero uno in many areas, including economy and social justice.
"Let prosperity flourish in the homes on the occasion of the new year and let there be light of joy in all our lives," he said in his greetings.
TNCC president K S Alagiri, AMMK leader and independent legislator TTV Dhinakaran and Makkal Needhi Maiam founder Kamal Haasan also extended their new year greetings.