The Rio de Janeiro club confirmed on Friday that the 65-year-old Jesus was leaving and Benfica later tweeted, "Welcome JJ."
Media in Brazil and Portugal have reported that he will be joining Benfica on a three-year deal worth €3 million a season.
Jesus will replace Bruno Lage, who resigned last month after winning one of five games since football restarted in Portugal after the hiatus caused by the new coronavirus pandemic.
"Our greatest thanks go to him and his backroom staff for all they have done and we hope they continue to enjoy the same enormous success they had with us," Flamengo said in a statement.
If he joins Benfica it will be Jesus's second spell at the Lisbon club he managed for six years between 2009 and 2015, winning three Portuguese league titles.
He came to Rio in June 2019 and has enjoyed a successful stint in the city, coaching Flamengo to the Brazilian first division title, the Copa Libertadores and Rio de Janeiro state championship, which they clinched on Wednesday.
With his heavy Portuguese accent and easily recognisable flowing grey locks, Jesus became a cult figure in Brazil, where adoring fans gave him the affectionate nickname Mister.
He led Flamengo to their most successful spell since Zico and Junior were at the club in the early 1980s, at one point taking them on a spectacular 29-game unbeaten run.
He is set to be charged with boosting Benfica's fortunes.
The capital club are second in the Portuguese league behind rivals FC Porto, who have already won the championship with two games to spare.