Mack signed the sheet from the Jaguars earlier today for a potential deal reportedly worth up to $42m (£25m), with $26m (£15.5m) guaranteed over five years.
The Browns had five days to decide whether they would match the offer before Mack became a Jaguars player, but they did so in a matter of hours to keep the two-time Pro Bowler in Cleveland.
They used their transition tag on 28-year-old this off-season, meaning that they would have the chance to match any offer that he received as a free agent.
The Jaguars' initial offer is understood to have included a clause which enables Mack to void the final three years without being subject to the team's franchise or transition tag.
Mack's guaranteed salary from the offer is the highest of any free agent this off-season and will make him the highest-paid centre in the league, with the former first-round Draft pick in line to make $10m (£6m) in his first season and $8m (£4.8m) every season after that.