Italy has been without a fully functioning government for nearly a month since former prime minister Matteo Renzi withdrew his Italia Viva party from Conte's coalition, which also included the M5S and centre-left Democratic Party (PD).
He also confirmed Luigi Di Maio as foreign minister, Roberto Speranza as health minister, Lucia Lamorgese as interior minister, Lorenzo Guerrini as defense minister and Dario Franceschini as culture minister - all keeping their roles in the previous government.
Mario Draghi, credited with saving the euro as president of the European Central Bank at the height of the eurozone crisis, will become Italy's new prime minister with a cabinet comprising a broad base of political parties and technocrats.
Confidence votes in both houses enabling him to take office will be a formality.
Results are expected after 7 p.m., the 5-Star official website said.
The post of justice minister has been given to Marta Cartabia (independent), of defense minister to Lorenzo Guerini (Democratic Party), of economy and finance to Daniele Franco (Bank of Italy director general), of economic development to Giancarlo Giorgetti (Lega), of agriculture policies to Stefano Patuanelli (M5S, he was responsible for economic development in the previous government), of ecological transition to Roberto Cingolani (independent), of transport and infrastructure to Enrico Giovannini (independent), of labor and social policies to Andrea Orlando (PD), of education to Patrizio Bianchi (independent), of universities and research to Cristina Messa (independent).
Nicknamed "Super Mario", Mr Draghi has significant support... for now.
"I swear to be loyal to the Republic", recited Draghi, the former head of the European Central Bank, as he stood before President Sergio Mattarella in the ornate presidential palace in a ceremony broadcast live on television.
Italy must also finalize its plan on how to use over 200 billion euros in grants and low-interest loans it is set to get from the EU's COVID-19 Recovery Fund.
M5S, the biggest party in parliament which began life as an anti-establishment movement, was split over whether to support a government led by an unelected technocrat. Another three are from the The League, the right wing party lead by Matteo Salvini who has in the past strenuously declared himself anti-immigrant and anti-European.
Mr Draghi was contacted after Mr Conte failed to cobble together enough support for a third coalition government.
Draghi was expected to present a list of ministers to Mattarella, before being formally sworn in on Saturday.
Their main priority will be to work out how to spend over €200bn (£175bn; $240bn) of European Union recovery funds to rebuild from the pandemic. However, many in Italy will be disappointed by the lack of women - of the 23 names, only eight are women.