Menezes replaces another former Brazil coach, Vanderlei Luxemburgo, who was fired on Monday after winning six of 19 games in charge of the Belo Horizonte club.
"This is the realisation of an old dream," the 53-year old former Gremio, Corinthians and Flamengo manager told the Cruzeiro website (www.cruzeiro.com.br).
"Within hours I will be with the team and starting work to get the recuperation going."
Cruzeiro were one of the most dominant teams in Brazil during 2013 and 2014 but sold many of their best players before this season and then fired Marcelo Oliveira, who had taken them to those titles, after a poor start to the campaign.
Luxemburgo replaced him but also struggled and the club are 16th in the table, one place above the relegation zone.
Menezes was Brazil coach between 2010 and 2012 and previously won the second division with Gremio and Corinthians. He also lifted state titles with both clubs.
(Reporting by Andrew Downie; editing by Ken Ferris)
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