Cleveland is sending a fourth-round pick this year (123rd overall) and seventh-round pick in 2019 to Miami for Landry, as first reported by MMQB and confirmed by ESPN.
The Browns are also working on a new contract for Landry, and a deal is expected to get done, according to a source.
Landry expressed excitement for his new team's offensive potential, tweeting: "Y'all better understand s--- about to get SERIOUS... ON MY MAMA."
The trade can become official on Wednesday at 4 p.m.
"Once I played my four years [in the league], a lot of things were out of my control," Landry told reporters Friday night prior to the inaugural Jarvis' Jam to benefit the Cystic Fibrosis Foundation in Miami. "The four years that I did have the opportunity to play for the Miami Dolphins, I left it all there, and I don't have any regrets about that.
"I'm excited about the next chapter in my life."
On a busy day for the Browns, they have also agreed to trade a third-round draft pick to the Buffalo Bills for quarterback Tyrod Taylor, a source tells Schefter.
The Browns are badly in need of a receiver. As a group, the team's wide receivers had seven touchdowns in 2017; Landry had nine. Kenny Britt, who was released in December, tied for the team lead in touchdowns for wide receivers with two (with Rashard Higgins and Corey Coleman). Higgins and Ricardo Louis led the Browns' wide receivers with 27 catches.
Landry is a sure-handed receiver who led the league in catches in 2017 with 112; all Browns receivers had 134. ESPN Stats & Information reports the Browns have never had a 100-catch receiver. Landry missed 1,000 yards by 13 but had 1,136 and 1,157 yards the previous two seasons. In four seasons, Landry has 22 receiving touchdowns. The Browns as a team had 15 receiving touchdowns last season.
Only Antonio Brown (471) and Julio Jones (411) have more receptions than Landry's 400 since he debuted in the NFL in 2014. Last season, Browns receivers caught 57 percent of the passes thrown to them; Landry has caught 71 percent in his career. He has been to the Pro Bowl three times.
The Dolphins placed the non-exclusive franchise tag on Landry on Feb. 20, the first day teams could issue the designation to pending free agents. After meeting with Landry's agent at the scouting combine in Indianapolis, the Dolphins gave the wide receiver permission to seek a trade. At least five teams expressed interest in Landry, including the Baltimore Ravens and Chicago Bears, a source told ESPN's Jeremy Fowler.
He was ejected in the Dolphins' season finale against the Buffalo Bills after he was an instigator in a fourth-quarter brawl. Coach Adam Gase called the incident "embarrassing."
On a busy day for the Browns, they have also agreed to trade a third-round draft pick to the Bills for quarterback Tyrod Taylor, a source tells Schefter.