Beisel played for the Chiefs from 2001-2004. The former Kansas State player most recently was with the Arizona Cardinals after a year in New England.
Engram began his NFL career with the Chicago Bears in 1996 and went to the Seattle Seahawks in 2001. He has caught 645 passes for 7,690 yards with 35 touchdowns, and has returned two punts for touchdowns.
Copper has played in 63 games with five starts during stints in Dallas, New Orleans and Baltimore. He also has 41 tackles while playing on special teams.
Terms of the deals announced Tuesday were not disclosed.