The US investment firm has been cleared to purchase the Italian Champions.
The terms of the deal state that the original owners, Elliott, a U.S. private equity group, will retain a minority investment and seats on the board. Milan recently won the Italian Serie A league title for the first time in 11 years.
RedBird founder and managing partner Gerry Cardinale said: "We... are excited to play a role in the club's next chapter as it returns to its rightful place at the very top of Italian, European and world football."
RedBird is also an investor in Fenway Sports Group, the owner of Liverpool and the Boston Red Sox baseball team. The group also has a controlling stake in the French club, Toulouse.
Cardinale said: "RedBird's investment philosophy and track record in team ownership has shown that football clubs can be successful on the pitch and sustainable off it."
Overseas investors have targeted Italian clubs due to cheaper valuations compared with those of England's Premier League and rivals in major European leagues.
The statement from the club added that the transition to new ownership will take place over the summer. The deal should close no later than September.
In 2018 when Chinese businessman Li Yonghong failed to meet obligations linked to financial packaging for the purchase of the team, Elliott took over the club.
Elliott also made a statement that its continued involvement with the club is a show of support for RedBird and added that the leadership of the club would stay intact.
Former Arsenal executive Ivan Gazidis is the club's CEO and Paolo Maldini, a former player is the club's Technical Director.