Wickremesinghe's United National Party (UNP) fell seven seats short of an absolute majority in the 225-member legislature in Monday's election when he saw off a challenge by the island's former president Mahinda Rajapakse.
Rajapakse had been standing as a candidate of the United People's Freedom Alliance (UPFA) which is officially led by Sirisena, even though the two men are now arch rivals.
While Rajapakse and a rump of his hardcore supporters are expected to remain on the opposition benches, another faction loyal to Sirisena is going to link up with the UNP, according to one of its leaders.
"We will support the formation of a national government, at least for a period of two years," Duminda Dissanayake told reporters after meeting Sirisena in Colombo.
Officials said Wickremesinghe was expected to be sworn in by the president at his sea-front office on Friday morning and his new cabinet could include some of the defectors.
The break-up of the UPFA had been widely expected given the splits between the factions loyal to Sirisena and Rajapakse who surprisingly lost a January presidential election after nearly a decade in power.
Sirisena had been an ally of Rajapakse, serving as health minister before splitting from his mentor and running against him for the presidency.
Read: Ex-Sri Lanka leader Rajapakse concedes election defeat
After winning the contest in January, Sirisena then turned to Wickremesinghe's UNP to lead a minority government.
But after its programme was consistently blocked in parliament where Rajapakse's followers remained in the ascendant, Sirisena decided to call elections a year ahead of schedule to break the logjam.
How many of the 95 UPFA members who won seats will join the government is not yet known. Rajapakse has indicated that he does not want to be the formal opposition leader but will instead be a backbencher.
Sirisena wants to reverse many of the constitutional changes brought in by Rajapakse which gave huge powers to the president.
Wickremesinghe's government is likely to introduce legislation to establish independent commissions to run the police, public service and judiciary.
Parliament is due to open on September 1.
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