The 1994 World Cup winner, who also worked as an assistant to Brazil coach Dunga from 2006-10, replaces Dorival Junior who was sacked at the weekend for refusing a wage cut proposed by the club.
"Jorginho is a professional who fits the profile desired by the new directors - he is young, studious about football, shows great leadership and has an identity with the history of the club," said Flamengo on their website.
"In addition the contract which has been signed with the new coach is in complete synchronisation with the model of financial responsibility and meritocracy which the directors have been implementing."
Jorginho also played for Brazil at the 1990 World Cup and was part of the team that won the Copa America in 1989.
He joined Flamengo as a 20-year-old and spent five years there before moving to Bayer Leverkusen and then Bayern.
Jorginho later played for Kashima Antlers, Sao Paulo and Vasco da Gama.