Wickremesinghe took his oath before President Gotabaya Rajapaksa at a ceremony in the president’s office on Thursday.
The president’s brother, Mahinda Rajakapsa, resigned as the PM on Monday following violent attacks by supporters on peaceful anti-government protesters. His resignation automatically dissolved the Cabinet, leaving an administrative vacuum.
Mahinda has since fled the capital Colombo and taken refuge at the Trincomalee naval base on the country's east coast.
The president’s selection of Wickremesinghe is seen an attempt to end violence triggered by the crisis and restore international credibility as the government negotiates a bailout package with the International Monetary Fund.
'Collapse beyond redemption'
Sri Lankans have suffered months of severe shortages of food, fuel and medicines -- as well as long power cuts -- after the country burnt through foreign currency reserves needed to pay for vital imports.
The central bank chief warned Wednesday that the economy will "collapse beyond redemption" unless a new government was urgently appointed.
The central bank almost doubled key interest rates and announced a default on Sri Lanka's $51-billion external debt as part of the policy shift, officials said.
Sri Lanka is facing its worst economic crisis since gaining independence from Britain in 1948. The crisis is caused in part by a lack of foreign currency, which has meant that the country cannot afford to pay for imports of staple foods and fuel, leading to acute shortages and very high prices.
Thousands of demonstrators have hit the streets across Sri Lanka since April 9 seeking the resignation of the Rajapaksa brothers.