The Italian president turned to Mr Draghi - whose illustrious career has earned him the nickname “Super Mario” - after parties failed to come up with a new coalition.
Mr Draghi said he was confident he would be able to find backing for a new administration.
The 73-year-old said he accepted the mandate knowing that Italy faces the multiple challenges of the coronavirus pandemic, a national vaccination campaign and an economic recession.
It was “a difficult moment” for the country, he said.
Mr Draghi has been set the task to form a new government to replace outgoing prime minister Giuseppe Conte's coalition of the 5-Star Movement and Democratic Party (PD).
In late January, Mr Conte resigned after a key coalition ally withdrew its support over his handling of the coronavirus pandemic and economic crisis in a bid to form a new coalition.
Talks aimed at salvaging the coalition failed on Tuesday, after which Mr Draghi agreed to step in to try and form a new government.
There was no guarantee that the highly respected economist would be able to muster sufficient support, with the largest party in parliament, the anti-establishment 5-Star Movement, immediately ruling out its backing.
The 5-Star, which has formed the backbone of Italy's last two coalition governments, has repeatedly railed against the concept of technocrat governments.
However, centre-left PD signalled it was ready to support Mr Draghi.
The alliance of right-leaning parties led by Matteo Salvini's League, which leads in opinion polls, said it preferred to go to early elections two years ahead of schedule, but would listen to Mr Draghi's proposals "without prejudice".
The League and the PD are sworn political enemies who have repeatedly vowed that they would never join a majority together.
A plausible scenario may see several parties abstaining in votes of confidence to ensure Mr Draghi can launch a government.
He has been widely credited with saving the euro zone from collapse in 2012. He was at the ECB from 2011 until 2019. Before that, he was the governor of the Bank of Italy.
Additional reporting by Reuters
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