Mr Wickremesinghe's United National Party (UNP) coalition won 106 seats in Monday's parliamentary election, just 7 short of a simple majority in the 225-member assembly but enough to form a government.
"We will also form the Cabinet thereafter," former Finance Minister Ravi Karunanayake said.
He was certain to receive the majority support from Rajapaksa's United People's Freedom Alliance (UPFA) which has 95 seats. The minority Tamil National Alliance swept the ethnic Tamil-majority Northern and Eastern provinces with 16 seats.
The 66-year-old veteran reformist was handpicked by President Maithripala Sirisena to lead a minority government after the ouster of longtime president Mahinda Rajapaksa in January.
A group of Sirisena supporters is likely to join a broad-based national unity government led by Mr Wickremesinghe.
Mr Wickremesinghe became prime minister for the first time in May 1993, when a suicide bomber assassinated president Ranasinghe Premadasa. He got his second chance in 2002, when he was credited with pulling the country out of recession.
Addressing a gathering yesterday, Mr Wickremesinghe said he will continue the mandate for good governance given in parliamentary polls and work together with all parties in a national government for 2-3 years.
"The parliamentary elections of August 17 confirms the January 8 revolution," he said, referring to the presidential election held in January which ousted the former President Mahinda Rajapaksa. "We can't turn back."
Mr Wickremesinghe, a nephew of Sri Lanka's first executive president, said he will build a consensus on the new government's national policy.
"I have got a mandate to put before parliament our plan so that we could arrive at a consensus and build a national framework within which we will do our policy," he said.
"This new approach requires all parties to work together, either in the government holding ministerial positions or in parliament through the oversight committees," he added.
"We will also be having district development co-ordination boards headed by the MP to carry out the decentralised development and the bodies which will have civil society without politicians, the 'grama rajya' committees which will cluster the villages as well as the advisory councils which will consist of civil society," he said.
A total of 196 members have been elected for a five-year term while 29 will be appointed based on the national proportion of votes polled by each party.
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