With almost 100% of the vote counted, his PB movement, only set up 4 months ago, won 44.7% and has secured a majority of 135 seats in the 240-seat parliament. It is the first time since 1997 that a single Bulgarian party has sufficient seats to govern alone.
Ex-prime minister Boiko Borisov's GERB party came second with 13.4%, with the liberal PP-DB coalition third with 12.8%.
The election was called after the previous government tried to push through a controversial budget in December, prompting mass protests which Radev, as president, supported.
"People rejected the self-satisfaction and arrogance of old parties and did not fall prey to lies and manipulation. I thank them for their trust," Radev said, in his victory speech.
He promised to build "a strong Bulgaria in a strong Europe".
"What Europe needs right now is critical thinking, pragmatic actions and good results, especially to build a new security architecture and … recover its industrial power and competitiveness. That will be the main contribution of Bulgaria to its European mission," he said.
Radev, 62, is seen as a pragmatic, somewhat pro-Russian leader, who has criticised EU sanctions, and called for constructive dialogue with the Kremlin.