The Seahawks confirmed the trade in a press release Tuesday.
Clemons appeared in 16 games for the Eagles last season, registering three sacks. Clemons began his career with the Washington Redskins in 2003.
Tapp, a second-round pick by the Seahawks in 2006, has totaled 18 sacks in four seasons with the team. Tapp recorded a career-low 2.5 sacks last season and started just five of 16 games.