Valeriu Strelet, deputy leader of the ruling Liberal Democratic party, and his new cabinet received the backing of a majority of lawmakers in the country's parliament.
Former prime minister Chiril Gaburici quit the job in June over allegations he faked his high school diploma.
In a speech to legislators, Strelet pledged to tackle widespread corruption after some USD 1 billion vanished in a banking scandal that rocked the nation.
The European Union swiftly congratulated Strelet on his appointment and looked forward to "intensive cooperation with him and his government".
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"Fraud of unseen proportions in the banking sector generated a chain reaction that destabilised the economic situation and led to a drop in the value of our currency," Strelet, 45, said.
Strelet promised also to strengthen political and economic ties for with the European Union and try to push ahead with Moldova's attempts to enter the 28-country bloc.
Last year, the government signed a historic EU association agreement despite pressure from its former Soviet master Moscow.
A spokesperson for EU foreign policy chief Federica Mogherini added in a statement that "reform of the justice sector and the fight against corruption need real decisive action."
Moscow slapped the largely agricultural country with a ban on its fruit imports in apparent retaliation for its shift towards the West.
Strelet said that he hoped to help "normalise" ties with Moscow.
Russia maintains thousands of troops in Moldova's breakaway region of Transdniestr, and has for years provided money to prop up the impoverished region of 500,000 people, which is home to some 180,000 Russian nationals.