Samak Sundaravej, leader of the PPP, said the party, formed by Thaksin's allies from his disbanded Thai Rak Thai (TRT) party, would form Thailand's next government.
"It is a victory for this country," Samak told a news conference, adding that he would "certainly be prime minister".
PPP's closest rival, the Democrat Party, was tipped to win 166 seats, with five smaller parties dividing up the rest, Thai television also reported.
Samak said that he would form a coalition after falling short of a full majority.
However, the leader of the Democrat Party said he would not be part of any coalition with the PPP.
"If PPP succeeds in forming a coalition, the Democrat Party is ready to become the opposition. If the PPP fails, then the Democrat Party is ready to form its own coalition," he told AFP news agency.
Thaksin 'dominant figure'
The military-backed Thai government dissolved the TRT and banned Thaksin from politics for five years after they seized power in a bloodless coup in September 2006.
But though he lives in self-imposed exile in London, Thaksin remains a dominant figure in Thai politics.
Analysts say the outcome of the election is unlikely to resolve divisions between Thaksin's supporters, largely drawn from the rural masses, and those ranged against him.
Panitan Wattanayagorn, from Thailand's Chulalongkorn University, said:
"People are expecting that the return of democracy is going to take place today.
"Although the new government is expected to be a coalition government, comprising of at least two or three more parties.
"No one is expecting one single party to win the election today. In a house of 480 seats, no one single party will likely gain more than 240 seats in this election."
The PPP draws most of its support from farmers, the majority of Thailand's 64 million population, who remember Thaksin's efforts to boost the rural economy.
The party has embraced the policies that won Thaksin two landslide victories and intends to bring him home if it wins a majority in parliament.