Terms weren't disclosed.
Engram and Copper will add experience to a young Kansas City offense that features third-year wide receiver Dwayne Bowe and new quarterback Matt Cassel, who recently was traded to the Chiefs from the New England Patriots.
Engram was selected by the Chicago Bears in the second round (52nd overall) of the 1996 draft and spent five seasons with the team before joining the Seattle Seahawks in 2001. Engram had 399 receptions and 18 touchdowns in eight seasons with the Seahawks, including six catches for 70 yards against the Pittsburgh Steelers in Super Bowl XL and career-highs in receptions (94) and receiving yards (1,147) in 2007.
Last season, Engram missed the first three games with a cracked bone in his right shoulder. He returned to catch 47 passes for 489 yards in 13 games for an injury-depleted Seahawks offense.
In five seasons with the Dallas Cowboys, New Orleans Saints and Baltimore Ravens, Copper has played in 63 games, five of them starts. He caught 46 passes for 600 yards with six touchdowns and returned 26 kickoffs for 502 yards during that time.
Beisel, an eight-year NFL veteran, will provide experience for a relatively young Chiefs defense. After being taken by Kansas City in the fourth round of the 2001 draft and spending four seasons with the team, Beisel made stops with the New England Patriots (2005), with whom he played alongside new Chiefs linebacker Mike Vrabel, and the Arizona Cardinals (2006-08), for whom he started in Super Bowl XLIII.