The performance, exceeding opinion poll forecasts, is one of the strongest results for a single party in a generation and could end, for now, the chronic instability that led to eight elections in five years.
Radev's Progressive Bulgaria party had 44.7 per cent of the vote after 91.7 per cent of ballots were counted, suggesting it could rule alone, but he has not ruled out a coalition with a pro-European group or a smaller party.
Progressive Bulgaria's tally put it far ahead of the pro-European We Continue the Change-Democratic Bulgaria (PP-DB) coalition with 13.2 per cent, and the long-dominant GERB party, led by former prime minister Boyko Borissov, at 13.4 per cent.
"This is a victory of hope over distrust, a victory of freedom over fear, and finally, if you will, a victory of morality," Radev told a press conference late on Sunday.
A eurosceptic and former fighter pilot opposed to military support for Ukraine's war effort against Moscow, Radev stepped down from the presidency in January to run in the parliamentary election after mass protests forced out the previous government in December.
He rode a wave of frustration with political instability in the Balkan nation of 6.5 million, where voters are sick of corruption and veteran parties that have dominated politics for decades.
Radev's campaign drew comparisons with Hungary's pro-Kremlin former prime minister Viktor Orban when he talked about improving ties with Moscow and resuming the free flow of Russian oil and gas into Europe.
He also criticised the European Union for relying too heavily on renewable energy.
However, Radev has been vague on policy and it is not yet clear how much he will change foreign policy in Bulgaria, a NATO member on the EU's southeast flank which joined the euro zone in January - a move Radev has criticised.
On Sunday, he said he would be willing to work on judicial reform with PP-DB and that Bulgaria would "make efforts to continue on its European path".
Bulgaria has developed rapidly since the fall of communism in 1989 and joined the European Union in 2007.
Life expectancy has risen sharply, unemployment is the lowest in the EU, and the economy has greater safeguards since adopting the euro.
But it lags EU countries in other metrics.
The cost of living has become a particular issue since Bulgaria joined the euro.
The previous government fell amid protests against a new budget proposing tax increases and higher social security contributions.
