The Texans also agreed to terms with cornerback Charles James and offensive lineman Jeff Adams.
Lechler, who turns 40 in August, played the past three seasons with the Texans after spending his first 13 years with the Oakland Raiders. He is the NFL's career leader with a 47.5-yard gross average. In 2015, Lechler averaged 47.3 yards, with a 38.8-yard net.
Novak, 34, signed with the Texans as a free agent in late September. He connected on 29 of 31 extra points and 18 of 21 field goals.
James, 25, was a key player for the Texans on special teams. He didn't make the opening day roster but returned during the season. He made 19 tackles in nine games as a cornerback.
Adams, 26, suffered a knee injury in Week 2 and went on injured reserve. He had been starting at left guard.