He thanked the people of the state for supporting the TDP-led government and its development agenda.
However, the opposition YSR Congress (YSRC), which lost the bypoll, said the setback was "temporary".
"Thanking people of Nandyal for showing their trust in TDP's governance. Will create a Smart Nandyal by following our motto 'People First'," Naidu said in a tweet after his party's Bhuma Brahmananda Reddy was declared winner in the bypoll.
"People have endorsed development agenda, upheld values in public life. Rejected and punished negative politics & disorderliness," the chief minister tweeted.
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Naidu also thanked Prime Minister Narendra Modi who congratulated Brahmananda Reddy and the TDP over the victory.
"We're happy to see that people of Nandyal have reflected their belief in our model of governance," the TDP president added.
Meanwhile, YSR Congress president Y S Jaganmohan Reddy said it would be a "mistake" for Naidu to claim victory in Nandyal.
He dared the chief minister to make all 20 MLAs, who defected from the YSRC to the TDP, resign from their posts and face fresh elections.
"One can then call it a referendum (on the state government)," the Leader of Opposition remarked.