Nearly three months after inconclusive elections on March 4, Di Maio and Salvini finally sealed a deal during a meeting at the Rome parliament on Thursday.
Italy on Thursday was awaiting a decision from right-wing leader Matteo Salvini on whether to join a last-ditch attempt to form a government and avoid snap elections that would be focused on membership of the euro zone.
"If the markets fear that Italy will exit the euro, it's because someone spread the news", said Luigi Di Maio, the leader of the Five Star Movement.
The anti-establishment 5-Star Movement and the anti-euro League have been emboldened by the president's dismissal of their government in favour of an unelected group of technocrats.
If, as expected, Cottarelli fails to win parliamentary backing, he would simply ferry Italy to elections that would most likely be held in September or October.
Italy's president has tapped politically inexperienced law professor Giuseppe Conte to be the premier who will head Italy's first populist government.
It had spiked to $1.1728 earlier on Monday after Italian President Sergio Mattarella rejected a vocal critic of the single currency as economy minister. The upshot is that Cottarelli's technocratic government team is ready, but that he and Mattarella are giving more time for the populist parties to seek an agreement, the official said.
"We are going to work hard to fulfil all of the political goals included in our government contract", the Prime Minister-appointed said in a short speech after the meeting.
A former International Monetary Fund official tapped to lead Italy's government until a new election could be held has stepped aside, paving way for political government of populists.
European stock markets made a modest recovery and returns on Italian government bonds fell back on Wednesday as fears over political turmoil in the eurozone's third-largest economy eased.
The deal followed an extraordinary few days in which Di Maio called for Mattarella to be impeached, Conte and another prime minister-designate were tasked to form a government and failed, before Conte was reinstated on Thursday evening.
The rare move by the president to veto the choice of finance minister sparked fury from both populist parties, who say they will reject cottarelli's nomination in parliament.
"We are not in the market", Salvini said when asked about the possibility of reopening negotiations, calling for elections as soon as possible. "It's a lie invented by Mattarella's advisors", Di Maio said in a live video on Facebook.
Italy's 10-year bond yields surged to over 300 basis points higher than Germany's - a sign of surging investor doubts over Italy's financial stability. The 5-Stars, by contrast, polled 32%.
"I will read the composition of the government", Giuseppe Conte, who will be sworn in Friday as prime minister with the rest of his Cabinet, said late Thursday.
Di Maio was said to be wary about having another far-rightist as well as Salvini as his partner, since polls show the M5S has been bleeding voters it gained from the centre-left Democratic Party (PD) on March 4 because of the possible new government's rightward drift.
United States futures are trading flat ahead of the open on Thursday, with Europe mostly a little higher as negotiations continue to avoid another election in Italy.
The earliest date at which elections could happen is July 29th, if Mattarella dissolves parliament on Wednesday.