NFL Network first reported the deal.
Byrd played for Arizona last season, catching 32 passes for 359 yards and one touchdown. He has a track-and-field background, running a 4.28 time in the 40-yard dash at his 2015 pro day at South Carolina.
The Patriots had one of the slower groups of skill position players last season, so adding speed brings a different dynamic to the wide receiving corps, with Byrd projected to fill a similar No. 4-5 role as Phillip Dorsett in recent seasons.
The Patriots on Tuesday also re-signed outside linebacker Keionta Davis. He played in six games for the team in 2018, making three starts, before spending the entire 2019 season on injured reserve.