Terms of the deal weren't disclosed.
McGowan, who missed most of the 2008 season because of an ankle injury, was signed by the Bears in 2005 as a rookie free agent out of the University of Maine. He appeared in 25 games, 13 of them starts, in Chicago.
McGowan will bolster New England's group of safeties. If free agent Rodney Harrison doesn't return, Brandon Meriweather, a first-round draft pick in 2007, and four-year veteran James Sanders likely will start for the Patriots, with 2009 second-round pick Patrick Chung contributing when he can.
Also on Tuesday, the Patriots released punter Tom Malone, who had stints on the team's practice squad in 2006 and 2008.
The Associated Press contributed to this report.