Palaniswami congratulated Kovind for his "resounding victory."
"I wish to convey to you my own felicitations and also those of the people of Tamil Nadu for a historic tenure in Rashtrapati Bhavan," he said in a letter to the NDA candidate.
Panneerselvam expressed "great joy" on Kovind winning the presidential polls.
"Having been elected as the first citizen of India, we wish Mr Ramnath Kovind name and fame due to his skill and service," Panneerselvam said in a statement.
Both the Amma and Puratchi Thalaivi Amma factions of the ruling AIADMK, led by Palaniswami and Panneerselvam, respectively, had supported Kovind in the July 17 poll held to elect the president.