The move came hours after a Sri Lankan court turned down an appeal to allow the disputed prime minister and his cabinet ministers to carry out their duties, officials said.
The country was taken by surprise when Sirisena sacked Wickremesinghe on October 26, nearly two years before his five-year term was up and called a snap election for January 5.
Rajapaksa resigned on Saturday as a government shutdown loomed.
According to reporters, after taking oath, the UNP leader will arrive at Temple Trees where a ceremony has been organized, with the participation of the MPs of the United National Front.
Rajapaksa resigned on Saturday as PM after the Supreme Court declared that the dissolution of Parliament by Sirisena was "illegal".
The prime minister, who refused to leave his Colombo residence throughout the crisis, emerged to greet crowds.
United Kingdom judge critical of Indian banks in providing loans to Vijay Mallya
Notably, the 62-year-old is being investigated for fraud and money-laundering by the Indian enforcement agencies. During the hearing India was able to convince the court that the argument advanced by Mallya was false.
In an unexpected move, Maithripala Sirisena had sacked Ranil Wickremesinghe and appointed Mahinda Rajapaksa as the Prime Minister on October 26, engendering an overnight constitutional crisis and paralysing the government.
President Maithripala Sirisena had refused to bow to pressure as the country drifted, declaring he would never reappoint Wickremesinghe and deriding his once-ally in public speeches as their alliance imploded.
Mahinda Rajapaksa's son Namal Rajapaksa on Friday tweeted that his father would resign as the prime minister of Sri Lanka. His party and its allies have a simple majority in Parliament and have argued from the beginning that President Sirisena's actions were unconstitutional. When Sirisena's decision was contested, he dissolved Parliament and called for a snap parliamentary election in January.
Sirisena was largely supported by Wickremesinghe's UNP in the January 2015 presidential elections and their parties went on to form a coalition government but, in recent months, differences have emerged between the two sides.
However, the Supreme Court overturned his decision and halted the preparations for snap polls.
Cabinet Ministers are expected to be sworn in tomorrow or the latest by Tuesday.
Assuring the President that the UNP would not be party to any impeachment process against him, Premadasa extended an olive branch to work together in the future, quoting from Buddhist scripture. He said since a general election can no longer be held, the UPFA cannot implement any of the measures they had planned to take "to prevent the country from becoming another Greece".