In a statement, outgoing president Benigno Aquino III’s spokesman said: “Our people have spoken and their verdict is accepted and respected.
“The path of good governance … is already established as all presidential candidates spoke out against corruption.”
Former interior secretary Mar Roxas, who was running second behind Mr Duterte in the unofficial vote count following Monday’s election, conceded defeat.
Using his rival’s nickname, he said: “Digong, I wish you success. Your victory is the victory of our people and our country.”
One of Mr Duterte’s harshest critics, Senator Antonio Trillanes IV, also conceded that the mayor – known for his off-colour sexual remarks and pledges to kill criminal suspects – had emerged the unquestioned winner.
MR Duterte, 71, has not spoken publicly since casting his vote on Monday, and remained at his home in Davao, on the southern main island of Mindanao.
But results from a semi-official count gave him an unassailable lead, thrusting him into national politics for the first time after 22 years as mayor of Davao and a government prosecutor before that. In those two jobs, Mr Duterte gained recognition by going after criminals, although he was also accused of carrying out hundreds of extrajudicial killings. That earned him the nickname “Duterte Harry”, a reference to the Clint Eastwood film character with little regard for rules.
Mr Duterte has also been compared to Donald Trump, the US Republican presumptive presidential nominee, for his propensity for inflammable statements.
In the separate election for vice-president, the son of late dictator Ferdinand Marcos was trailing by a narrow margin behind Leni Robredo, who is backed by Mr Aquino.
During the three-month campaign, Mr Duterte made audacious promises to eradicate crime and corruption within six months. His explosive outbursts and curses against the inequality and social ills that bedevil the Filipino everyman resonated with the public, and his major political rivals clearly underestimated this until he began to take a strong lead in opinion polls in the final weeks of the campaign.
Mr Duterte captured attention with speeches peppered with obscene jokes about sex and rape, and anecdotes about his Viagra-fuelled sexual escapades, along with undiplomatic remarks about Australia, the US and China, all key players in the country’s politics.
He has not articulated an overall foreign policy, but has described himself as a socialist wary of the US-Philippine security alliance. He has worried members of the armed forces by saying that communist rebels could play a role in his government.
But his campaign manager, Peter Lavina, said the brash image, the obscene jokes and the outlandish promises were a strategy to attract voters.
“That’s part of the game… you have to find ways for you be in the headlines,” he said.
Mr Duterte displayed his softer side early yesterday when he visited his parents’ tomb in a Davao cemetery to pay homage to them.