A team spokesman announced the move Saturday morning, minutes before the Seahawks started training camp. Morey was a Pro Bowl selection in 2008 with Arizona, and he signed a free-agent contract with Seattle this offseason.
The 34-year-old has been a leader in raising awareness of head injuries. Last season, he was named co-chair of the NFL Players Association's concussion and traumatic brain injury committee.
Morey went to Brown, then played nine seasons for the Patriots, Steelers and Cardinals.