Luxemburgo replaces Ney Franco, who was sacked after the club picked up just seven points from their first 11 league matches. They currently sit bottom of the 20-team Serie A.
"The new coach has signed a deal until December 2015 and his first match will be in the derby against Botafogo next Sunday at the Maracana," Flamengo said in a statement posted on their website.
Luxemburgo becomes Flamengo's third coach this season.
He played for the Rio side in the 1970s and has since been involved in coaching more than 30 teams. He first led Flamengo in 1991 and was re-hired in 1995 and 2010. Only once did he last more than a year in the job.
His previous coaching job was with Flamengo's rivals Fluminense last year.
(Reporting by Andrew Downie; editing by Toby Davis)
