The former Real Madrid, Inter Milan and AC Milan player had last managed Cameroon, where he was sacked in July 2019.
He has joined Corinthians on a contract until the end of the 2027 season, the club said in a statement.
Corinthians, who are a point above the relegation zone in the Brazilian Serie A, sacked previous manager Fernando Diniz on Wednesday.
Seedorf had terminated his contract with Botafogo to retire as a player and take up his first managerial role at Milan in January 2014.
He took over at Milan when they were 11th, and helped them finish eighth, before being dismissed in June. He later coached Shenzhen and Deportivo La Coruna.
Corinthians visit second-placed Palmeiras later on Sunday.
