He won 62.7% of the votes, the state election commission said on Thursday.
Elections were held on Wednesday to pick a successor to Boris Trajkovski, the "peacemaker" president who died in a plane crash two months ago,
His rival Sasko Kedev of the VMRO party got 37.3%, it said, after almost all ballots were counted. Turnout at 53.4% passed the 50% minimum of the 1.7 million voters needed for the vote to be valid.
International observers were due to publish their findings later on Thursday.
Crvenkovski, who was also premier from 1992 to 1998 and whose Social Democrats sought to strengthen their grip on power, outpolled Kedev in the first round of voting two weeks ago, but failed to secure an absolute majority.
The VMRO said major ballot-stuffing took place and that it would not accept the result. "We will never recognise the self-proclaimed president," said Kedev, 42, adding that his party would present what he called solid evidence of fraud.
Crvenkovski's spokeswoman rejected the allegations. "This was a fair and democratic election," said Radmila Sekerinska.
"We will never recognise the self-proclaimed president"
candidate, opposition VMRO
State election commission head Stevo Pendarovski declined to comment on the dispute, saying his office would rule on the issue if it received a formal complaint.
Crvenkovski, if confirmed will be Macedonia's third president since independence from the former Yugoslavia 13 years ago.
He has vowed to work for his country's membership of the European Union, which Skopje applied to join last month. He also aims to cement peace after an ethnic Albanian guerrilla insurgency brought Macedonia close to civil war three years ago.
The outcome looked likely to please Western powers which had feared that voter apathy might end in failure to pick a new head of state and plunge the poor, ethnically divided Balkan country into political uncertainty and delay crucial reforms.
"Macedonia will continue on the path aimed at European Union and NATO membership, which is good," said one envoy in Skopje.
The diplomat said there had been some voting irregularities but he did not believe they had affected the outcome or that there would be a repeat election, as VMRO has called for.
"I can't imagine that happening," he said.