With more than 98% of votes counted, Mr Yanukovych had a 2.7% lead over his rival, PM Yulia Tymoshenko, media said.
Mr Yanukovych called on Mrs Tymoshenko to quit, but she refused and is expected to challenge the result.
International observers described the vote as an "impressive display of democratic elections".
"For everyone in Ukraine, this election was a victory," the observers, led by the Organisation for Security and Cooperation in Europe, said in a statement, Reuters news agency reported.
"It is now time for the country's political leaders to listen to the people's verdict and make sure that the transition of power is peaceful and constructive."
The BBC's Richard Galpin in Kiev says favourable judgements by the electoral commission and international observers will make it much more difficult for Mrs Tymoshenko to challenge the outcome.
She has postponed a news conference on the result until Tuesday.
The results suggest a remarkable comeback after Mr Yanukovych was swept aside by the 2004 "Orange Revolution".
Under the 59-year-old former mechanic, Ukraine's foreign policy is expected to become more pro-Russian.
Our correspondent says a Yanukovych win would be an extraordinary indictment of the pro-Western Orange Revolution leaders' failure to deliver on their promises, which has left people deeply disillusioned.
AT THE SCENE
Richard Galpin, BBC News, Kiev
It could still be several days before the official and final result is announced, but Mr Yanukovych now knows he has been elected Ukraine's next president.
Five years ago he was the villain of the Orange Revolution. He was humiliated in his bid to lead the country, the election then was ruled to have been fraudulent.
It is possible the result of Sunday's election will also be challenged. His rival in the race, Prime Minister Yulia Tymoshenko, has still not admitted defeat.
If he is able to take power, Mr Yanukovych is certain to develop much closer relations with Russia. While the leaders of the Orange Revolution have been in government, Ukraine has shifted decisively away from Moscow and much closer to the West.
Politics in Ukraine has now gone full circle, our correspondent adds.
Mr Yanukovych was a presidential candidate in the last election in 2004, which was found to have been rigged in his favour.
Mrs Tymoshenko's impassioned leadership of the subsequent street protests that swept him from power - and thrust her to office, along with Viktor Yushchenko - made her an international celebrity.
But the prime minister - once a fierce critic of Russian involvement in Ukraine - has close ties with her Russian counterpart, Vladimir Putin, who said at a recent meeting she was someone he could "do business with".
Incumbent President Viktor Yushchenko lost in the first round of the election last month.
With more than 98% of votes counted, Mr Yanukovych was ahead with some 48.55% of the vote, with Mrs Tymoshenko at around 45.85%, according to media reports.
It is set to be a narrower margin of victory than Mr Yanukovych had been hoping for, but he has already congratulated his supporters and said he will deliver the change the country is yearning for.
WHY UKRAINE MATTERS
Russian Black Sea fleet based in Sevastopol, Crimea
Most Europe-bound Russian gas piped through Ukraine
Large ethnic Russian and Russian-speaking minority in Crimea and industrialised east
Strong nationalist, pro-Western sentiment in west
Aspirations for EU and Nato membership, though latter strongly opposed by Russia
Why the future was not Orange
Profile: Viktor Yanukovych
Profile: Yulia Tymoshenko
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The opposition leader reportedly said it was time for his rival to quit.
"I think that Yulia Tymoshenko should prepare to resign. She understands that well," Interfax-Ukraine quoted him as saying in a television interview.
"In any case, I believe such a suggestion will be put to her."
But Mrs Tymoshenko, 49, showed no sign of standing down.
In a news conference earlier, she said her team was conducting a "parallel count" and urged them to "fight for every result, every document, every vote".
Mr Yanukovych won last month's first round of voting, finishing 10 percentage points ahead of Mrs Tymoshenko.
Yulia Tymoshenko at a rally in Kiev on 5 February 2010
Yulia Tymoshenko traded claims of foul play with the Yanukovych camp
She has threatened to take her supporters to the streets if defeated, saying the protests could be larger than those of the Orange Revolution.
Sunday's vote came after a bitter mud-slinging campaign in which real policy issues and debate appeared to have been forgotten, says our correspondent.
On Saturday, Mrs Tymoshenko's political bloc accused Mr Yanukovych's Party of Regions of blocking her supporters from overseeing the vote in the eastern Donetsk region.
Mr Yanukovych's camp hit back with allegations that some supporters of the prime minister had been tampering with ballots in an attempt to get votes from eastern Ukraine disqualified.
President Yushchenko - who came fifth in last month's first round - led a series of bitter personal attacks on former ally Mrs Tymoshenko during the campaign.
His working relationship with the prime minister over the last five years was poisoned by bickering as Ukraine became engulfed by an economic crisis, with its GDP plummeted 15% last year.