The 54-year-old replaced former Portugal coach Paulo Bento, who was sacked after a poor run of results, Cruzeiro said on Tuesday, reports Xinhua.
Menezes left Cruzeiro after three months in December to take charge of Shandong Luneng, but he resigned in June with the club mired in the Chinese Super League's relegation zone.
Cruzeiro are currently 19th in Brazil's 20-team Serie A standings with just 15 points from 16 matches.
Menezes will begin his latest spell with the Belo Horizonte outfit on Sunday in an away clash against fourth-placed Santos.
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