The three-year deal could average between $2-3 million per season.
Gregory visited with the Patriots over the past two days.
The 5-foot-11, 195-pound Gregory has been with the San Diego Chargers since entering the league as a rookie free agent out of Syracuse in 2006.
Gregory, 29, has played in 85 games during his career, initially emerging as a speedy special-teams presence before working his way into the starting lineup (31 career starts). He started a career-high 13 games last season, but one line of thinking is he was playing out of position alongside free safety Eric Weddle.
Some believe Gregory is better suited for a free safety role, which is one of the Patriots' offseason priorities to pair with Patrick Chung. The Patriots had a revolving door at safety last season.
Gregory's ability to play in the slot in sub packages, as well as his special teams background, should fit in well with the Patriots.
In 2010, Gregory was suspended four games for a violation of the league's policy on performance-enhancing substances.
In other moves:
• Offensive lineman Dan Connolly, who has started 24 regular-season games over the past two years, has agreed to a new contract with the Patriots, The Boston Globe reports. The 6-foot-4, 313-pound Connolly will turn 30 on Sept. 2. He can play center and both guard positions. Dan Koppen, the team's starting center since 2003, is also a free agent this offseason.
Slater, a 2011 Pro Bowler, was one of the team's top free agents. The 2008 fifth-round draft choice served as one of the team's captains last year.
Meanwhile, Harrison (6-3, 316) returns to the Patriots after a one-day stint during the 2011 season.
The 2008 third-round draft choice of the Chicago Bears was signed by the Patriots on Oct. 14, 2011, when there were some injury concerns leading into the team's Oct. 16 game against the Dallas Cowboys. But Harrison was released Oct. 15.
The former Arkansas product appeared in 37 games for the Bears, where he played alongside Patriots defensive end Mark Anderson, totaling 55 tackles and three sacks.