"It is really admirable that from a humble beginning in Gujarat, you have risen to the top position of India through your innate intelligence, hard and sincere work," he said in a statement.
The 90-year old DMK chief also congratulated him on his unanimous election as leader of the BJP Parliamentary party.
Referring to Modi's acceptance speech in Parliament when the BJP leader said his regime would be dedicated to the growth of poor, youth and women, he said, "this great nation expects you very eagerly to realise this lofty ambition."
"On behalf of the DMK, I convey my best wishes to you for a happy and satisfying Prime Ministerial tenure, fulfilling the aspirations of all sections of this vast country."
Just before beginning his poll campaign in February, Karunanidhi had praised Modi as "a hard worker and my good friend too."
When the results were declared on May 16, he had greeted BJP and Modi on the "big win" and vowed to continue to work to win people's confidence.
However when he began his poll campaign on April 5 at Coimbatore, Karunanidhi, had castigated the BJP leader and said he has "no place" in Tamil Nadu.