The deal is for one year, a league source told ESPN NFL Insider Adam Schefter.
The agreement came on the same day that the club released No. 3 quarterback Garrett Gilbert, a first-year player out of Southern Methodist.
Brady has been suspended for the first four games of the 2015 season as a result of the findings of an investigation into allegations that the Patriots illegally deflated footballs in the AFC Championship Game.
Brady has appealed his suspension. That hearing before commissioner Roger Goodell will be heard June 23.
The 6-foot-2, 225-pound Flynn has had two different stints with the Green Bay Packers (2008-11; '13-14), while also spending time with the Seattle Seahawks (2012), Oakland Raiders (2013) and Buffalo Bills (2013).
He has seven career starts, and the Patriots are familiar with the first of his career: In 2010, filling in for injured Packers quarterback Aaron Rodgers, Flynn was 24 of 37 for 251 yards, with three touchdowns and one interception in a 31-27 loss to New England.
Last season he appeared in seven games for the Packers, with most of his action coming late in blowout games.
He attempted only 16 passes, completing eight of them for 66 yards without a touchdown pass and with one interception.
Flynn, who spent his first four years with the Packers, returned to Green Bay midway through the 2013 season after Rodgers broke his collarbone. Flynn went 2-2 as the Packers' fill-in starter that season.
In addition to releasing Gilbert, the Patriots confirmed that tight end Tim Wright was waived, along with undrafted rookie receiver Zach D'Orazio. The team signed three undrafted free agents: linebacker D.J. Lynch (Bowling Green) and tight ends Jimmay Mundine (Kansas) and Logan Stokes (Louisiana State).
ESPN.com's Field Yates and Rob Demovsky contributed to this report.