Mr Stolojan was Romania's second PM after the fall of communism in 1989
Romanian President Traian Basescu has asked a former World Bank economist to form a new government after last month's inconclusive general elections.
Theodor Stolojan has 10 days to secure parliament's approval for his cabinet.
Mr Stolojan, who was prime minister in 1991-92, is a member of the opposition Liberal Democrat Party (PDL).
The PDL edged the rival opposition Social Democrats in the 30 November polls, and the two parties have been in talks on forming a possible coalition.
President Basescu said on Wednesday that Mr Stolojan was "capable of handling the effects of the economic crisis and has the necessary authority to ensure the smooth functioning of government".
Mr Stolojan's PDL and the Social Democrat Party (PSD) were less than 1% apart in the polls, each securing about a third of the vote.
The ruling National Liberals (PNL) polled only 19%.
It was the first general election since Romania joined the European Union at the beginning of last year.
President Basescu said before the elections that he would prefer a centre-right government.
Squabbles between the PDL and the PNL, which is led by outgoing Prime Minister Calin Popescu Tariceanu, wrecked their coalition in 2007.
Since then Mr Popescu Tariceanu's minority government has been tacitly supported in parliament by the PSD and the ethnic Hungarian party (UDMR), which will also be represented in the new parliament with 6% of the vote.