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Orban, 56, a former transport minister, must now receive backing from the fragmented parliament as the poor, corruption-plagued EU-member struggles to overcome months of political instability.
President Klaus Iohannis named Orban -- a familiar face in Romania's political landscape for the past two decades -- after holding two rounds of consultations with parliamentary groups.
Speaking alongside Iohannis, Orban vowed to "respect the rule of law and judicial independence".
"I am putting all my experience and my energy to work toward the public interest," he said.
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Lawmakers last week voted narrowly in favour of a no-confidence vote against the government of Viorica Dancila's Social Democratic Party (PSD).
Since taking power in late 2016, the PSD has faced massive protests and criticism from Brussels over controversial judicial reforms seen as helping politicians to escape corruption sentences.
The designation of Orban was expected after his party successfully spearheaded the no-confidence vote.
Orban, whose father comes from Romania's Hungarian minority, has ten days to form a cabinet and ask for parliament's approval, which is far from a done deal given that PNL has only 95 of 465 seats.
"I hope the political decision-makers understand that we are in a political crisis and that we have to quickly come up with a solution," said Iohannis.
The liberals are counting on the votes of the five other parties which supported the no-confidence vote to see their government installed, with some trading strict conditions in return for their support.
But one of them -- the centre-right Union Save Romania (USR), which this year surged in popularity -- has already called for snap elections, arguing that a government with a limited mandate will not have enough traction to take on profound reforms.
The PSD, which have 201 seats, said they will not support the new government.
"We won't vote Iohannis's government," PSD chief Dancila said on Tuesday, adding that PSD lawmakers will not attend the plenary session during which the next government will ask for a vote.
Iohannis has said he does not oppose snap elections, but insisted the Romanian constitution makes such a scenario highly unlikely.
The next parliamentary elections are scheduled for late 2020.
One of the main challenges of the next government will be to write next year's budget, complicated by an explosion of public spending in recent months as the PSD struggled to stay in power.
The political shift comes one month before the first round of presidential elections, scheduled for November 10.
Incumbent Iohannis, seeking a second term with the support of PNL, is seen as a clear favourite -- even more so now after former premier Dancila, who is also running, lost executive power and plunged her party into crisis.