But cutting Gregory, the Patriots save $2.85 million in cap space, bringing their estimated cap room to around $12.35 million.
"I had a great time in New England and respect the organization a lot," Gregory told ESPNBoston.com. "It was time well spent and I learned a lot. Obviously, you never want to get released from a team. There will be other opportunities, and it's on good terms.
"I have no hatred toward anyone. The fans were great. The whole atmosphere out there was unbelievable. It was a great time of my life that I'll always remember."
The eight-year veteran spent the past two seasons with New England, playing in 26 regular-season games. Gregory played 72.7 percent of the defensive snaps last season and was touted by teammates as being one of the smartest players they've been around.
Duron Harmon, the Patriots' 2013 third-round pick, is the next man on the safety depth chart. The 6-foot-0, 205-pound Harmon played 36.9 percent of the defensive snaps last season, starting three games when Gregory was sidelined with a broken thumb.
The Patriots could add to the position in free agency or the draft, with free agency the deeper and more expensive option. At this point, Harmon would seem to have the inside track on a top role. Third-year player Tavon Wilson, who slid down the depth chart in 2013, is also at the position. Veteran Adrian Wilson, who spent last year on injured reserve and seemed to jeopardy of not making the club at the end of preseason, is also on the roster.