The club has endured a turbulent spell with managers of late, with three already hired this year alone and outgoing boss Jorginho being fired after just 14 games.
Menezes, meanwhile, has been out of work after his two-year spell in charge of his country came to an end back in November.
"Flamengo can confirm the hiring of coach Mano Menezes," a club statement read. "The board would like to put on record its appreciation of Rubro-Negro fans for supporting the club through the process."
Meanwhile, Menezes has spoken of his pride at taking over the club and his excitement about the challenge ahead.
"I'm very proud," Menezes wrote on Twitter. "To be the coach of Flamengo is my new great challenge. It's an honor."
Speaking to the club's official website, meanwhile, the 51-year-old Menezes spoke of his desire to turn the team into a competitive force.
"We must compete better against our opponents, and if we can improve our togetherness as a club, the Rubro-Negro will be much stronger."
Flamengo is currently 14th in the Brasileiro, having won just one of its opening five games.