He had already been picked to succeed outgoing leader Nguyen Tan Dung at the Communist Party's congress in January.
In his inaugural remarks reported by local media, he promised to lead the country to prosperity.
He now governs the country together with Communist Party general secretary Nguyen Phu Trong and President Tran Dai Quang, who were endorsed last week.
Wednesday's inauguration was seen as a formality as Mr Phuc, the former deputy prime minister, was the only candidate for the position following his selection in January. He won more than 90% of the vote in parliament.
He pledged to protect the country's sovereignty and also to improve the business climate and crack down on corruption, reported Thanh Nien News.
Vietnam is one of the fastest-growing economies in Asia, but is also facing high public debt, a budget deficit, and territorial challenges from China.
The country saw economic reform under outgoing president Nguyen Tan Dung, who lost a battle to retain power during the party congress.
Mr Dung had gunned for the position of general secretary, pitting himself against Mr Trong, but ultimately withdrew when he failed to win sufficient support among delegates.
Vietnam's new prime minister Nguyen Xuan Phuc has been formally voted in by parliament.