The party allied to ousted and exiled former leader Thaksin Shinawatra is set for a major victory in Thailand's general election, partial results say.
Outgoing Prime Minister Abhisit Vejjajiva has already conceded victory to his rival, opposition leader Yingluck Shinawatra.
She will become Thailand's first female prime minister.
Yingluck Shinawatra is the sister of Thaksin Shinawatra, who was ousted in a military coup in 2006.
With 80% of votes counted, official results indicated that Ms Yingluck's Pheu Thai party would win 251 seats, giving it a majority in parliament.
"It is now clear from the election results so far that the Pheu Thai party has won the election, and the Democrat Party concedes defeat. I would like to congratulate the Pheu Thai party for the right to form a government," Mr Abhisit said on national TV.
'Much work ahead'
When exit polls were shown on television, Pheu Thai supporters erupted in celebration at the party headquarters in Bangkok.
Yingluck Shinawatra said: "Let's wait for the official results. I will tell you how I feel tonight."
Mr Thaksin told the BBC from his self-imposed exile in Dubai that it was clear the Thai people had voted for change.
"They want to see reconciliation, we want to have reconciliation," Mr Thaksin told the Newshour programme.
All parties will have to respect the voters' decision, he said.
Mr Thaksin, whose government was toppled in a military coup in 2006, said the military should also "be listening to what the people think".
Asked whether he would now be returning to Thailand, the former prime minister said he was in "no hurry".
"I want to see reconciliation really happen," he said. "I want to be part of the solution, not part of the problem."
The BBC's Karishma Vaswani in Bangkok says both sides have vowed they will respect the result but there is concern that their supporters will not and that there could be a return to violence.
The past few years have seen street protests, airport closures and clashes between the supporters of the two main groups, which our correspondent says have tarnished the country's economy and reputation for being a bastion of democracy in south-east Asia.
Last year, protesters shut down parts of Bangkok for two months in a bid to force the government to resign. When the army stepped in to clear the capital's streets it degenerated into violence, leaving 91 people dead.
Many of the red-shirt demonstrators were supporters of Mr Thaksin.
Official results are expected in the late evening.
Exit polls, released as soon as voting ended, suggested a big majority victory for Pheu Thai.
More than 40 parties fielded 3,832 candidates for the 500-seat lower house of parliament, the House of Representatives.
In a two-tier system of voting, 375 legislators will be elected by constituency, while 125 candidates will be chosen from lists according to the proportion of votes each party receives nationwide on a separate ballot. There are some 47 million eligible voters.
Yingluck Shinawatra was one of the first to vote at a school in Bangkok. She smiled and showed her ID card to television cameras before casting her ballot.
She said: "Thank you, supporters, who have been so kind to me."
Our correspondent says Ms Yingluck is a political novice, and her popularity seems to rest on the fact she is campaigning on the policies of her brother, who many believe is Pheu Thai's real leader.
He is living in Dubai to avoid a corruption conviction.
Mr Abhisit had also voted in Bangkok and urged people to "cast votes quickly because this election is very crucial for our country".
He had said a vote for Pheu Thai was a vote for Mr Thaksin, and pointed out the party's own slogan was "Thaksin thinks, Pheu Thai does".
He said the country must "get rid of the poison of Thaksin".
With Pheu Thai's win all but confirmed, analysts say all eyes will once again be on the military, which has regularly intervened in the political process. Army chief Gen Prayuth Chan-ocha on Thursday stressed that he would stay neutral.
Thailand has had 18 attempted or successful military coups since democracy was established in 1932.
Our correspondent says there is a lot at stake.
Whoever wins will have to reunite a divided nation and try to heal Thailand's wounded democracy, she adds.