Stephenson was suspended two games by the NFL on Friday for violating the league's policy on substance abuse.
Signed by the Browns in March, Stephenson will miss the first two games of the regular season and be eligible to return to the team on Sept. 17.
The punishment will cost Stephenson $294,117 in salary and bonuses, according to Spotrac. Stephenson also was fined $84,435 by the Browns for missing this week's mandatory minicamp.
The 29-year-old Stephenson spent the last two seasons with the Denver Broncos, starting a career-high 12 games in 2016.
A third-round pick of Kansas City in the 2012 NFL Draft, Stephenson appeared in all 16 games in three of his first four seasons with the Chiefs, making 21 starts.
Stephenson remains eligible to participate in all offseason workouts and preseason practices and games.