The trade was earlier reported by ESPN's Adam Schefter.
Mingo, 25, was the sixth overall pick in the 2013 draft and has seven sacks in three seasons.
The Browns did not pick up his fifth-year option, and he was scheduled to become a free agent after this season.
The Patriots are hoping he will provide some additional pass rush.
Mingo was drafted by the Browns when Mike Lombardi was general manager. Lombardi spent the 2014 and 2015 seasons as an assistant to the Patriots coaching staff and remains a confidant to head coach Bill Belichick.
The Patriots are deep at their end-of-the-line position, which is where Mingo projects to play, as Jabaal Sheard and Rob Ninkovich are starters and Chris Long, Shea McClellin and Trey Flowers are also on the depth chart.
Ninkovich is rehabilitating from a torn triceps muscle that could sideline him into the regular season.
The Patriots now have acquired the No. 6 and No. 7 overall picks from the 2013 NFL draft in separate trades. Earlier this offseason, the Patriots acquired offensive lineman Jonathan Cooper from the Arizona Cardinals in the trade that sent Chandler Jones to Arizona. The Browns selected Mingo with the sixth overall pick, and Cooper was picked by the Cardinals with the next selection in the first round.
Mingo never found a role in Cleveland. He had been tried as a pass-rusher, then as a pass defender, without much effectiveness at either. This training camp the Browns even tried him at inside linebacker, but his status with the team was summed up by Sashi Brown, the team's vice president of football operations, on Thursday morning when he met with Browns media in Tampa: "He's showing up on [special] teams. We'd like to see him show up more in the defense."
Mingo started 16 games in three seasons, his sack total going from five to two to zero. The Browns' recent first-round picks have not met expectations, as none of Cleveland's four first-rounders taken between 2011 and 2013 is still with the team. Mingo was traded; running back Trent Richardson is out of the NFL; quarterback Brandon Weeden is a backup with Houston; and defensive tackle Phil Taylor is with the Broncos.
Of the team's eight first-round picks from 2011 through 2015, only three are with the team, and one of them -- cornerback Justin Gilbert -- is fighting for a roster spot. Gilbert was drafted in the first round with quarterback Johnny Manziel in 2014.
The Patriots also previously lost a 2017 fourth-round pick due to the penalties handed out as part of Deflategate.
The Browns have acquired these 2017 picks: the Eagles' first-round pick, the Titans' second-round pick, the Colts' seventh-round pick and now the Patriots' fifth-round pick. They also own Philadelphia's 2018 second-round pick.
ESPN Patriots reporter Mike Reiss and ESPN Browns reporter Pat McManamon contributed to this report.