Brown, 26, joined Rovers from Batley ahead of the 2013 season, and went on to score nine tries in 16 appearances.
He had an option in his contract to stay at Craven Park for a second year, but has opted to join the Centurions.
Rovers CEO Mike Smith said: “On behalf of everyone at the club I’d like to thank Alex for the contribution he made both on and off the field during his time with us. The option was there for him to stay but he has decided to move on and does so with our very best wishes for the future.”
A Jamaica international, Brown has also previously played for Keighley, Rochdale and Huddersfield.
He is perhaps most remembered for the two late tries he scored in Batley’s 25-24 2010 Northern Rail Cup final win over Widnes.