"Thank you to everyone for breaking a political deadlock," Samak Sundaravej, the PPP leader, said at a press conference.
"I am really relieved that now there's nothing more to worry about," he said.
Although the country will learn later in the week who the new prime minister will be, Sundaravej, 72, is the clear frontrunner.
Sundaravej, whose temper is notorious, served as Thaksin's deputy in the mid-nineties and is accused of being a proxy.
"Thank you to everyone for breaking a political deadlock"
Samak Sundaravej, PPP leader
Sundaravej said parliament will open on Monday and could choose a new prime minister within the week.
Bhumibol Adulyadej, the Thai monarch, must then give his official approval - a formality that normally takes a few days.
Although the PPP's victory was threatened by legal challenges last month, the supreme court dismissed serious charges against them on Friday.
Election officials also announced they had settled most of their investigations when it came to voter fraud.
Surayud Chulanont, Thailand's caretaker prime minister and the man the military installed after the 2006 coup, told Al Jazeera that he hopes Sundaravej would lead the country to reconciliation.
"I always said that whoever gained the most votes had an absolute right to rule," he said.
Blow to generals
The newly elected government delivers a blow to the royalist generals in the military, who had wanted to erase Thaksin's flamboyant political and corporate dynasty.
Thaksin and 110 of his top lieutenants were banned from politics after the bloodless coup.
His once-dominant Thai Rak Thai [Thais Love Thais] party was also disbanded.
The PPP government is expected to welcome Thaksin back to Thailand from exile by April.
He has remained in Britain since the coup in a self-imposed exile.