Mr Boc is also a mayor of the Transylvanian city of Cluj
The leader of Romania's centre-right Liberal Democrats, Emil Boc, is being asked to form a new government, after a previous candidate turned down the job.
Party colleague Theodor Stolojan, 65, had initially been nominated as PM, but in a surprise move stood aside, saying the job should go to a younger man.
Mr Boc, aged 42, said he now hoped his cabinet would get parliamentary approval within a week.
His party edged the rival opposition Social Democrats in last month's polls.
The Liberal Democrats (PDL) and the Social Democrat Party (PSD) were less than 1% apart in the 30 November polls, each securing about a third of the vote.
The ruling National Liberals (PNL) polled only 19%.
At the weekend, the PDL and the PSD reached a preliminary deal on forming a coalition.
Mr Stolojan, who was prime minister in 1991-92, made his surprise resignation announcement in parliament on Monday.
Mr Stolojan was Romania's second PM after the fall of communism in 1989
"With this gesture, I want to give hope to a new younger generation of politicians, who can rise to the highest positions in the state," the former World Bank economist said.
After the announcement Mr Boc, a lawyer by training, promised to put together a government to lead Romania out of the current economic crisis.
"Our objective is to give Romania a stable and competent government," he said.
President Traian Basescu said he would now formally nominate Mr Boc as PM.
Mr Basescu - who led the PDL before becoming president - said before the elections that he would prefer a centre-right government.
It was the first general election since Romania joined the European Union at the beginning of last year.
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 after gaining 6% of the vote.