Jesus, 65, took the helm of Flamengo last year and led the club to three trophies in 2019, winning the Copa Libertadores, Brazilian Serie A and Campeonato Carioca.
The former Benfica boss confirmed he had agreed to a new deal on Tuesday, with reports suggesting he will earn around €4million.
"My representatives reached an agreement today with Flamengo's board of directors to renew my contract for another year," Jesus wrote on Instagram.
"My friendly relations with the entire squad, club structure and Flamengo's fans were decisive to touch my heart and spoke louder in my decision.
"Thank you all for your kindness and support."
Jesus has led Flamengo to 41 wins from 55 games since taking charge in June last year.
The Copa Libertadores success last year was Flamengo's first since 1981.