The much-travelled striker is now free to find another club, which would be the 11th of his career, after departing Rovers with a year left on his contract.
Best suffered an early injury after moving to Ewood Park from Newcastle in 2012 for £3m and then struggled to reclaim his place in the first team.
The 28-year-old was loaned out to Sheffield Wednesday in 2014 and last season had temporary spells at Derby and Brighton, for whom he made a combined total of 33 appearances without scoring a single goal.
He has also made seven appearances for the Republic of Ireland.
A statement on Rovers’ website read: “The club thanks Leon for his work and dedication during his time at Ewood Park and wishes him all the best for the future.”