Iohannis made the decision after days of consultations with parliamentary parties when only the opposition came with concrete proposals for the Prime Minister's position and even the Cabinet's composition, Xinhua news agency said.
The President stressed that the government, which will be installed in the coming weeks, will have a short term, until the Parliamentary elections.
"And, if it comes to the parliamentary elections, I repeat, I personally think that early elections are a very good solution," said Iohannis.
According to the Constitution, early parliamentary elections cannot take place before the Presidential election next month.
"I am honored to assume this responsibility on behalf of the National Liberal Party," said Orban after being appointed to organize a new government.
"We will give the Roman what they expect from us, namely honesty, competence, integrity, dedication in serving the public interest and solutions for the big problems that Romania faces today," he said.
"We will hold consultations with all the political groups with whom we have worked so well to ensure the success of the censure motion," said Orban earlier, after a party Executive Bureau meeting on Monday.
However, local analysts expressed doubts that Orban and his new cabinet may be supported, in the parliamentary vote of confidence, by all the parties that topped the Social Democratic Party government a week ago.
According to Orban, the future Cabinet that could be formed by his party, possible together with other parties, will be a much slimmer one, with no more than 16 ministries.
The outgoing Prime Minister leads a cabinet of 24 members.
Under the constitution, Orban has 10 days to form a government, and win a confidence vote in Parliament.
Orban, 56, has been chairman of the National Liberal Party since June 2017. He was minister of transport from April 2007 to December 2008 and a member of the Romanian Chamber of Deputies from 2008 to 2016.
( With inputs from IANS )