The Times Online reported Borisov's coalition was poised to take 117 seats in the 240-member Bulgarian parliament. The Socialists were expected to retain only 39 seats, continuing the trend started in 1990, in which Bulgarians have ousted the incumbent governing coalition at each election, the British news Web site said.
Official results of Sunday's general election were expected some time Monday.
Borisov, 50, told local television channel bTV his Citizens for European Development of Bulgaria party, commonly referred to as GERB from the party's Bulgarian name, had dealt a "smashing, annihilating" defeat to the Socialists.
The Sofia Echo reported Borisov struck a conciliatory tone toward Muslims during a news conference but warned those involved in corruption or other government abuses.
"For us, ethnicity does not play a role," Borisov said, adding Bulgarian Muslims have a role to play in the government of the country.
He said the new government would prosecute any corruption cases that took place under the previous government.
Nearly 7 million people were eligible to vote, the BBC reported.
Bulgaria last year lost access to some of its European Union funds for failing to deal with government corruption and organized crime. Bulgaria joined the European Union in 2007, with EU officials warning the nation's leaders to clean up the government.