Walter started 14 games opposite Andre Johnson last season and had 53 receptions for 611 yards and two touchdowns. He joined the Texans in 2006 and has 195 receptions for 2,470 yards and 15 touchdowns since arriving in Houston.
Walter, who has started 45 games in the last three seasons, signed with the Texans after three seasons in Cincinnati.
Turk averaged a franchise-best 42.8 yards per punt last season and landed 24 punts inside the opponents' 20-yard line. The 41-year-old spent the last three seasons with the Texans after a year in St. Louis.
Terms were not disclosed Monday.