Davis joined the Patriots on Monday, four days after being reinstated by the NFL from an indefinite suspension for a second violation of the league's substance abuse policy.
When the suspension was announced in February 2014, Davis said he was being punished for taking a supplement that included a banned substance. He says it wasn't for marijuana, which was the reason for his first suspension.
Davis, 29, played 72 games with the Redskins from 2008 to 2013. A second-round draft selection in 2008, Davis has 162 career receptions for 2,043 yards and 13 touchdowns.
Chandler signed a two-year contract in March with a maximum value of $5.3 million. Gronkowski and Chandler project as roster locks, so the addition of Davis adds another layer of competition to the No. 3 and 4 spots with Hoomanawanui, Wright and Derby, a sixth-round draft pick.
ESPN NFL Patriots reporter Mike Reiss contributed to this report.