Orban has 10 days from Iohannis' announcement on Tuesday to gain the support of parliament, which must approve the new government.
Orban's nomination comes after the Social Democratic government led by Viorica Dancila, beset by corruption scandals, lost a no-confidence vote in the legislature last week.
The PNL, as Orban's party is known, is the largest opposition group.
Orban said after meeting Iohannis that his administration would give Romanians what they look for in a "normal government, namely honor, competence, integrity, dedication to serving the public interest and solutions to the big problems Romania is facing today."
A parliamentary election is scheduled for late 2020.
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