The clubs met via video call on Wednesday and agreed on the start date that is aimed at completing the 12 games most Serie A sides have to play to finish off the season.
Players have been training individually at their clubs for a couple of weeks but they will now be able to train in groups as of Monday.
"Regarding the resumption of sporting activity, in accordance with the decisions of the Government and in compliance with the medical protocols to protect players and all involved personnel, the date of June 13 has been indicated for the resumption of the league," a Serie A statement said.
The government protocol mentioned in the statement sets out a different plan to the Bundesliga restart model, and in Italy if a player or member of staff tests positive for coronavirus beyond May 18 then the whole squad must go into quarantine for two weeks.
With the Coppa Italia also to complete from the semi-final stage, a June 13 start is planned to be able to complete both that and the league campaign before UEFA's deadline of August 2.
Italy has been one of the worst affected countries during the pandemic, and at least 19 Serie A players have tested positive for Covid-19, including players from Fiorentina, Sampdoria and Torino just last week.
Serie A was suspended on March 9 and with 12 games to go for most clubs, Juventus are top of the table as they chase a remarkable nine straight title - but they face a real fight this season with Lazio just a point behind.
Related content
Responsible gambling
We are committed in our support of responsible gambling. Recommended bets are advised to over-18s and we strongly encourage readers to wager only what they can afford to lose.
Sky Bet's responsible gambling tools are detailed here and if you are concerned about your gambling, please call the National Gambling Helpline on 0808 8020 133, or visit begambleaware.org.
Further support and information can be found at GamCare and gamblingtherapy.org.