The two veterans were released on Tuesday by Cleveland, which is transitioning from a 4-3 front to a 3-4 scheme under new coach Rob Chudzinski and coordinator Ray Horton. Defensive end Frostee Rucker was cut on Feb. 5, the first move of the Browns' defensive makeover.
Gocong was expected to bolster the linebackers when he was acquired in 2010 from Philadelphia, and he did start 32 games.
But the 29-year-old missed last season after tearing his right Achilles in training camp. The Browns signed Gocong to a three-year, $16.8 million contract extension in 2011. He was scheduled to make $4.55 million next season.
Gocong had 141 tackles with 5½ sacks and three fumble recoveries in two seasons with Cleveland.
Young, 27, was signed as a free agent in 2011 after four seasons with New Orleans. In two seasons with the Browns, he made 19 starts, recorded 118 tackles and had four interceptions.
With Young no longer on the roster, free safety appears to be a major need as the Browns approach this month's NFL draft.
The Browns have been looking for a kicker since deciding not to re-sign Pro Bowler Phil Dawson, who signed a one-year deal with San Francisco. Bogotay kicked at Georgia for three seasons as a backup to Blair Walsh, who is now with the Vikings.
Norwood appeared in two regular-season games last season before a foot injury forced him to miss the final 11 games. He finished with 13 receptions for 137 yards, and had a career-high nine catches for 81 yards against the New York Giants on Oct. 7.
Yount handled all the long-snapping duties in 16 games last season.