The PPP won the December 23 polls, the first since Thaksin was toppled in a bloodless coup in September 2006, but was not left with a majority in the 480-seat parliament.
Their victory was threatened by legal challenges filed in the supreme court and dozens of vote fraud investigations by the Election Commission (EC).
But on Friday, the PPP was cleared as the supreme court dismissed the most serious charges against it and election officials announced they had settled most of their investigations.
The coalition would give a PPP-led government about two-thirds of the seats in parliament.
Twenty seats voided as a result of the EC's vote fraud investigations will be filled through by-elections later this month.
Pravit Rojanaphruk, a political analyst for Bangkok's The Nation newspaper, told Al Jazeera that the military still plays an influential role in politics.
He said: "The military wanted a say, as to who would become the defence minister, and last year, the military-appointed parliament passed a bill - the Internal Security Bill - which will give extra powers to the military.
"What we are seeing now, is a sharing of power between the PPP and the military."
Although the installation of an elected government brings some short-term political calm, few expect it to last.
Complicating the situation further is the prospect of Thaksin's return from exile, scheduled to take place in April.
Thaksin was barred from holding elected office for five years. But he has said that he could serve as an adviser to PPP.
Samak, however, is considered a divisive figure in Thai politics.
The PPP, which was organised after Thakin's Thai Rak Thai Party was dissolved by court order, has vowed to reinstate the populist policies that swept Thaksin's party into power largely due to his success in the country's rural areas.