The 60-year-old agreed to a four-year contract with the option of an extension, should Chile qualify for the 2022 World Cup, ANFA said in a statement on Monday, reports Xinhua news agency.
It added that Rueda, who has previously coached the national teams of Colombia, Ecuador and Honduras, will be at the helm of Chile's senior national squad and the national youth teams.
"We hope that Reinaldo Rueda achieves great things with the Roja, and that he passes on his experience and knowledge to our players at all levels," ANFA said.
Chile, the reigning Copa America champions, have been without a coach since October when Juan Antonio Pizzi departed after the team's failure to qualify for the 2018 World Cup.
Rueda joined Flamengo in August and guided the Rio outfit to sixth in Brazil's 20-team Serie A standings, earning them a berth in next year's Copa Libertadores, South America's version of the UEFA Champions League.
He also led the Rubronegro to the final of the second-tier Copa Sudamerica, which they lost to Argentina's Independiente.
Flamengo responded to the news by announcing former Brazil international midfielder Paulo Carpegiani as their new head coach. It will be the 68-year-old's third spell in charge of the Rio de Janeiro outfit.
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