The centre-right president Klaus Iohannis signed the official decree naming Grindeanu, a 43-year-old former communications minister, as the new premier.
Grindeanu now faces a confidence vote in parliament on his programme and cabinet nominees.
The nomination sought to put an end to a political crisis sparked when Iohannis rejected a previous candidate who would have been the country's first female and first Muslim prime minister.
The president offered no reasons for his rejection of Sevil Shhaideh, initially put forward by the Social Democrats (PSD), but there was speculation that it was due to her Syrian husband's background.
He is seen in Romania as a "disciplined soldier" within the PSD ranks and said himself in a recent interview that he had joined the party very young as an outlet for his leftist convictions.
The PSD had proposed the previously little-known Shhaideh after its thumping poll victory on December 11 when it won 45 per cent of the vote, enough to form a majority coalition with its partners ALDE.
Shhaideh, 52, who has only five months ministerial experience, is from Romania's small and long-established Turkish minority, but her Muslim faith is not thought to have been the problem.
Website HotNews cited unnamed sources as saying that the security services had "strongly cautioned" against Shhaideh's nomination because of the closeness of her husband and his two brothers to President Bashar al-Assad regime.
This might have made giving Shhaideh the necessary security clearances to be the NATO member's prime minister problematic.
PSD leader Liviu Dragnea had withdrawn his own bid to become prime minister because of a conviction that bars him from office.
"In our opinion the president is determined to set off a political crisis," Dragnea had warned. "If our conclusion is that it is in the country's interest to suspend Mr Iohannis, I won't hesitate."
However, any attempt by the PSD to remove the head of state would have been problematic because Iohannis was entitled to request a second proposal for premier.
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