The two teams exchanged undisclosed 2022 draft picks. ESPN’s Adam Schefter reported they’ll swap seventh rounders.
Blough was signed by the Browns this year as an undrafted free agent.
Blough completed 25 of 43 passes for 271 yards with two touchdowns and two interceptions this preseason.
Teams have until 4 p.m. eastern Saturday to get down to a 53-man roster.
Thursday afternoon, Dorsey acquired guard Wyatt Teller from Buffalo along with a 2021 seventh round pick for a 2020 fifth and sixth round pick.