Terms have not been reported.
Novak, 35, played last season on a one-year, $965,000 contract. He has played on five different teams in his nine-year NFL career; but he found success in his second season with the Texans.
Novak finished the regular season tied for second in the league in made field goals. His 35 made field goals represented a career high and a single-season record for the franchise. Novak made 16 straight field goal attempts from Nov. 13 to Dec. 24.
Novak said he wanted to return to Houston and was hopeful his agent could get a new deal worked out with the Texans.
Lechler, meanwhile, will enter the 2017 season at the age of 41. He didn't say at the end of last season whether he wanted to continue to play in the NFL.
Lechler finished the season ranked No. 6 in gross punting average, averaging 47.5 yards per kick.