Contract details were not released.
Charles, a running back, rushed 538 times for 3,328 yards and 36 touchdowns in three seasons at Texas. He will compete for the backup running back job behind starter Larry Johnson.
Cottam, a tight end, started in 38 games at Tennessee.
Just four days before training camp, the Chiefs have now signed eight of their 12 draft picks. But three of the four unsigned players are the team's top picks.
Copyright 2008 by The Associated Press