President Klaus Iohannis named Campeanu to lead a temporary administration ahead of talks with political parties, due to begin today, over who should form a new government.
Ponta quit yesterday after a horrific fire at a Bucharest nightclub left 32 people dead, prompting tens of thousands of people to take to the streets demanding a "profound change" in the government as a wave of grief and anger swept the country.
The embattled Social Democrat, who had been under pressure for weeks as he faces charges of fraud, tax evasion and money laundering, said it was right that top officials took responsibility for Friday's tragedy at the Colectiv nightclub.
Iohannis, a conservative who was elected in 2014 with a large youth backing, also said Thursday that in the wake of the protests he would consult with civil society representatives before forming the new government.
"I followed the protests and I have an important message for all those who were in the street on Tuesday and Wednesday," Iohannis told reporters.
"I saw you, I heard you and I will consider your demands."
Ponta's resignation failed to stop tens of thousands of protesters from spilling onto the streets again on Wednesday for a second night running.
"Our friends in the Colectiv disco were killed by a vile system."
New premier Campeanu said the interim government would continue to work on the country's 2016 budget plans, due to be submitted to parliament this month, even though it is not empowered to pass new laws.