He resigned in December as two crucial Supreme Court decisions made the former strongman's efforts to cling to premiership untenable.
The apex court later unanimously declared that the dissolution of Parliament by Sirisena was "illegal".
Mahinda won power in 2005 and went on to become South Asia's longest-serving leader. He became the country's youngest ever parliamentarian in 1970 at the age of 24.
The two brothers led a decisive campaign that helped end the island nation's three decade long civil war against the Liberation Tigers of Tamil Eelam (LTTE).
Earlier in the day, Prime Minister Wickremesinghe announced his resignation, days after the ruling party's candidate lost the presidential election to Rajapaksa.
Rajapaksa defeated Wickremesinghe's deputy Sajith Premadasa.
In a special statement in Sinhala language, the Prime Minister said that he had met President Rajapaksa on Tuesday and discussed the future of Sri Lanka's Parliament, Colombo Gazette newspaper reported.
He said that while his Government still has the majority in Parliament it was decided to respect the mandate given to Rajapaksa at the Presidential election and step down.
"I will step down to allow the new president to establish a new government. I will officially inform him of my decision tomorrow," Wickremesinghe said.
He has been the leader of the United National Party (UNP) since 1994 and served as Sri Lanka's prime minister for a total of three terms.
He was under pressure to quit and handover the government to the opposite camp after Rajapaksa won the presidential election on Saturday.
The UNP leader faced a revolt since Premadasa's defeat, a regular occurrence during the last 25 years whenever the UNP lost a major election.
Harin Fernando, a minister from the party's younger brigade, told reporters that they want Wickremesinghe to quit the party leadership and name Premadasa his successor for both the party leadership and the post of the main opposition leader.
"We will form our own party if he did not make the necessary changes this time," Fernando told reporters.
There will be a caretaker cabinet of 15 members to run the government until Rajapaksa will be constitutionally able to dissolve parliament after February 2020.
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