Before winning confirmation on a 295-133 vote, Grindeanu said he wanted a country "where people have the freedoms and rights that the vast majority of European citizens have."
President Klaus Iohannis swore in the new government of Social Democrats shortly after the vote, urging it to guarantee an independent justice system and the rule of law, and strengthen its position within the European Union and NATO.
The Cabinet includes an economist who had been poised to become the country's first female and Muslim prime minister.
But Iohannis declined to nominate Sevil Shhaideh, a political novice and member of Romania's small Muslim minority, after it emerged that her Syrian-born husband, who had worked at the Syrian agriculture ministry, had expressed support for President Bashar Assad on social media.
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There are concerns that the coalition government -- which has 26 ministers, four more ministerial posts than the previous technocrat-led government -- may seek to slow down Romania's anti-corruption fight.
Grindeanu also hinted at tempering the anti-graft fight, saying it should be "firm, but equally firm should be the defense of fundamental human rights."
An opposition leader, Raluca Turcan, said the Social Democrats were incapable of "governing in a European way" so long as they were led by Liviu Dragnea, an old-style politician who was disqualified to head the new government because of a conviction for election fraud.
Grindeanu said the government planned to raise the minimum wage, to hike pensions and student grants and make free medicine widely available.
Grindeanu also vowed to stop the "exodus" of thousands of Romanians, by creating better-paid jobs in Romania and reducing pork and tomato imports, which Romania produces locally.