The Patriots received a conditional sixth or seventh-round draft pick in 2016, a source told ESPN.
Mallett, 26, could have a bright future with the rebuilding Texans, who will enter this season with veteran journeyman Ryan Fitzpatrick as their starting quarterback.
To make room for Mallett on their roster, the Texans will waive quarterback Case Keenum, a source told ESPN. Keenum started eight games last season and had been battling rookie Tom Savage for a backup role behind Fitzpatrick.
The 6-foot-6 Mallett was drafted by New England in the third round in 2011 and had served as Tom Brady's primary backup in each of the last two seasons.
But Mallett was passed on the Patriots' depth chart this summer by rookie Jimmy Garoppolo, a second-round pick who impressed throughout training camp and the preseason.
Patriots coach Bill Belichick would not comment on the team's depth chart at quarterback following last Thursday's preseason finale against the New York Giants.
But Garoppolo played the entire game against New York, punctuating a stellar preseason during which he completed 46 of 79 passes for 618 yards, five touchdowns and one interception.
Mallett appeared in three games this preseason, completing 14 of 26 attempts for 161 yards, one touchdown and no interceptions.
ESPN Texans reporter Tania Ganguli, ESPN NFL Insider Adam Schefter, ESPN's Adam Caplan and ESPNBoston.com's Mike Reiss contributed to this report.