Rueda will replace Juan Antonio Pizzi, who resigned in October after the 2015 and 2016 Copa America champions failed to qualify for the World Cup finals in Russia.
"We took the necessary time to find the right alternative for our team," president of the Chilean football federation Arturo Salah said in a statement.
"A coach with experience at international level, who has qualified for World Cups and who has a trajectory at the sport's highest level."
Rueda, 60, has previous international experience as coach of Colombia, Honduras and Ecuador.
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He joined Flamengo last year after a successful spell with Atletico Nacional, whom he led to the Copa Libertadores in 2016.
His contract with Chile will run until the end of qualifying for the 2022 World Cup in Qatar and will be extended if the South American side make the finals.
Flamengo said Rueda will be replaced by Paulo Cesar Carpegiani, who has a long history with the Rio de Janeiro club as a player and coach.
(Reporting by Andrew Downie; Editing by Greg Stutchbury)
