The prime minister's message came immediately after Naidu, the ruling NDA's candidate, was declared winner in the vice presidential polls, bagging 516 votes out of total 771 votes cast.
The opposition's candidate Gopal Krishna Gandhi could only manage 244 votes.
"Congratulations to @MVenkaiahNaidu Garu on being elected India's Vice President. My best wishes for a fruitful & motivating tenure," Modi tweeted.
"I am confident @MVenkaiahNaidu will serve the nation as a diligent & dedicated Vice President, committed to the goal of nation-building," the prime minister added.