Hyde, who started five of six games, leads the Browns with 382 yards and five touchdowns this season.
Dorsey got a 2019 fifth-round pick in return. The trade is pending a physical.
The Browns signed Hyde this offseason to a three-year, $15.25 million contract as a free agent from San Francisco.
The trade clears the way for rookie running back Nick Chubb, selected 35th overall in the 2018 draft, to take over as the primary back.
Chubb is averaging 10.8 yards per carry, including touchdown runs of 63 and 41 yards at Oakland in Week 4. Subtract those two runs and the Georgia product is still averaging 4.9 yards per carry.
The acquisition of Hyde by the Jaguars fills the hole created by Leonard Fournette’s hamstring injury.