Perriman will sign a one-year contract that could worth up to $8 million and includes $6 million in guarantees, Rosenhaus told ESPN's Adam Schefter.
Perriman will replace Anderson as the Jets' deep threat. The deal also saves them at least $4 million on the 2020 salary cap, as Anderson reportedly will make $12 million in his first season with the Panthers.
Perriman set career highs across the board with the Tampa Bay Buccaneers in 2019, finishing with 36 catches for 645 yards and six touchdowns as he and quarterback Jameis Winston started clicking -- particularly on the deep ball -- later in the season.
With star receivers Mike Evans and Chris Godwin sidelined because of hamstring injuries, Perriman, who turns 27 in September, had a league-leading five touchdown catches over the final four weeks of the season. Three of those scores came in Week 15 against the Detroit Lions, for whom his father, Brett Perriman, played in the 1990s.
The Bucs, seeking a true speed threat to replace DeSean Jackson with little salary-cap space, signed Perriman last offseason to a one-year deal worth $4 million.
Before joining the Bucs, Perriman played a season with the Cleveland Browns and two with the Baltimore Ravens, who selected him in the first round of the 2015 draft. Overall, Perriman has 95 receptions for 1,561 yards -- an average of 16.4 yards per catch -- and 11 touchdowns.
He missed the 2015 season because of a partially torn PCL in his right knee. He was sidelined for training camp in 2016 because of a partially torn ACL and missed the preseason and one regular-season game in 2017 because of various injuries.
ESPN's Jenna Laine contributed to this report.