The Benetton family and the U.S. fund, who have joined forces through investment vehicle Schema Alfa, aim to take the Italian airport and motorway operator private by the end of this year. They are offering Atlantia's investors 23 euros per share and a proposed dividend of 0.74 euros a share.
The bid heralds a new phase for Atlantia which sold its domestic motorway unit earlier this year to draw a line under a political dispute sparked by a deadly bridge collapse in 2018.
The Benetton family, which already owns 33% of Atlantia, and Blackstone need to get the final go ahead from Italy's market watchdog Consob before they can launch the bid on the stock market.
The proposed bid needed Bank of Italy's greenlight because the central bank oversees some activities of Atlantia's digital toll payment unit Telepass.
(Reporting by Francesca Landini; Editing by Emelia Sithole-Matarise)