The team announced Monday that it had a deal with the 2008 Pro Bowl selection from the Arizona Cardinals. The 34-year-old was an alternate for last season's Pro Bowl.
Morey's specialty is punt and kickoff coverage.
Morey was a seventh-round draft choice by New England in 1999. He spent the past three seasons with the Cardinals and has made 151 tackles on special teams in 109 games.
He has led his team in special teams tackles five times in seven full NFL seasons. He has 11 career receptions as a wide receiver.