Hollister is out with a hamstring injury, which kept him sidelined six games. He missed two other games with a chest injury.
The team’s third tight end played only 59 snaps on offense and caught four passes for 52 yards. He played 97 snaps on special teams in eight games.
Anderson, 25, has spent the season on the Patriots’ practice squad. He played 28 regular-season games and two postseason games with the Texans.
He has 36 catches for 435 yards and two touchdowns in his career.
The Patriots also announced they signed defensive back A.J. Howard and offensive lineman Dan Skipper to the practice squad.