The deal, to be finalised in coming weeks, ends a dispute over the infrastructure group's motorway concession triggered by the deadly collapse of a motorway bridge in Genoa in 2018.
The Benetton family - best known for its retail clothing chain - owns 30% of Atlantia, which controls motorway unit Autostrade per l'Italia and airport operator ADR.
German insurer Allianz, France's EDF and China's Silk Road Fund bought a 12% stake in Autostrade in 2017.
Autostrade, which last year generated around 13% of Atlantia's core earnings, manages around half of Italy's motorway network under a concession contract due to end in 2038.
Here is a timeline of events over the last two years.
Aug. 14, 2018
A motorway bridge operated by Autostrade gives way sending cars and trucks hurtling 50 metres to the ground and killing 43 people in the port city of Genoa, in northern Italy.
The then transport Minister Danilo Toninelli tells Italian state television the disaster shows the dilapidated state of Italy's infrastructure and a lack of maintenance, adding that "those responsible will have to pay".
Aug. 17, 2018
The Italian government takes initial steps aimed at revoking Autostrade's motorway concession before its 2038 expiry date. Prime Minister Giuseppe Conte issues a statement blaming Autostrade for the poor upkeep of the network.
Sept. 28, 2018
The government approves the "Genoa decree" to appoint a special commissioner to reorganise the city's road system. The decree also states that Autostrade will be excluded from the works to rebuild the bridge, but will have to foot the bill.
A consortium comprising builder Salini Impregilo, now called Webuild, shipbuilder Fincantieri and inspection and engineering services group RINA start the works to build a new bridge to help connect Genoa with southern France under the project involving Genoa-born architect Renzo Piano.
Italian prosecutors launch an investigation into the safety reports compiled by SPEA, a unit of Atlantia, over five motorway bridges operated by Autostrade. SPEA, which was also in charge of safety monitoring on the Genoa bridge, denies allegations that it altered inspection reports for the viaducts.
Aug. 14, 2019
Grieving relatives ask Atlantia Chief Executive Giovanni Castellucci and chairman Fabio Cerchiai to leave an anniversary ceremony honouring the victims of the Genoa bridge disaster, adding it had been insensitive to invite them.
Sept. 17, 2019
Atlantia CEO Castellucci steps down after 13 years, bowing to pressure from the Benetton family, which says it has been shocked by allegations of falsified security reports regarding some of the viaducts run by Autostrade.
Dec. 24, 2019
The government approves new legislation aimed to make it easier and cheaper to revoke concessions to operate motorways. The measure cuts the amount the government must pay to a toll road company if a concession is revoked due to shortcomings on the part of the operator.
April 28, 2020
Workers lay the final section of the new bridge in Genoa pledging to open it to road traffic by the end of July.
July 8, 2020
A top Italian court rules against Autostrade, saying a law the government introduced in 2018 to exclude it from work to rebuild the Genoa bridge was not unlawful.
July 15, 2020
The government says Atlantia has agreed to gradually exit from its motorway unit Autostrade, to make room for state lender Cassa Depositi e Prestiti (CDP) and allied investors, bringing the motorway network back under state control.
(Reporting by Francesca Landini; Editing by Keith Weir and Emelia Sithole-Matarise)