The president's office announced on Thursday that law professor Mr Conte had accepted the role and would be sworn in on Friday afternoon with cabinet ministers.
Mr Conte read the list of ministers and told reporters in a brief statement: “We will work with determination to improve the quality of life of all Italians.”
The announcement demonstrated that president Sergio Mattarella has accepted the cabinet chosen by the anti-establishment Five Star Movement and League parties at their second attempt of forming a government.
Mr Mattarella last week vetoed the populists’ original choice for finance minister, the Eurosceptic professor Paolo Savona, threatening to scupper any coalition deal.
Mr Salvini will serve as the interior minister in Mr Conte’s cabinet, while Mr Di Maio will take over the industry ministry.
Mr Savona will be in government, but as European affairs minister, a less powerful role but one which will still allow him to negotiate with Brussels and speak on EU issues.
Giovanni Tria is now expected to be handed the key economy job in place of Mr Savona, who advocates the formation of a “plan B” to prepare the country’s exit from the eurozone.
Mr Tria, although critical of the European Union’s economic governance, has not touted the possibility of the country ditching the euro.
In recent articles he has called for a change in the EU’s fiscal rules to allow public investments to help growth and, like many mainstream economists, has criticised Germany’s persistently large current account surplus.
Global financial markets plunged last week as a second election dominated by a debate on Italy’s future in the single currency seemed likely to take place.
Five Star and the League – formally known as the Northern League – emerged as the two largest parties following the country’s general election in March, although neither were able to secure a majority.
In a joint programme announced under initial coalition talks, the parties revealed plans to scrap austerity measures and repatriate migrants, putting them on a collision course with Brussels.
The League, a right-wing anti-migrant populist party with its support mostly concentrated in the north, has said it wants to leave the eurozone as soon as politically feasible.
Five Star, founded by comedian Beppe Grillo, holds more ambiguous political stances and has rowed back in recent months on some of its more eurosceptic rhetoric.
Additional reporting by agencies
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