"Congratulations on the successful completion of three years in office as Prime Minister of India," Mr Palaniswami said in a letter to the Prime Minister.
"India has made great strides under your able, efficient and dynamic leadership. On this occasion, I would like to thank you for extending all co-operation and support to the government of Tamil Nadu," he said.
Mr Palaniswami also wished PM Modi many more years of good health to continue to serve the nation and people of India.
"I pray that the Almighty blesses you with many more years of good health to continue serving the nation and the people of India," he said.
On May 24, during his meeting with Modi at Delhi, Mr Palaniswami had invited PM Modi to be the chief guest at two events to honour late AIADMK stalwarts and former chief ministers M G Ramachandran and J Jayalalithaa.
For more stories on three years of the Modi government, click here
Get the latest election news, live updates and election schedule for Lok Sabha Elections 2019 on ndtv.com/elections. Like us on Facebook or follow us on Twitter and Instagram for updates from each of the 543 parliamentary seats for the 2019 Indian general elections.