The 23-year-old will join the club this week ahead of the 2018 season.
Head Coach Garth Brennan is pleased to have the opportunity to work with Cartwright.
“I’ve known Bryce since he was 17 and I’m so pleased that we can work together again,” Brennan said.
“I’ve seen him develop over the past seven years and I believe he is one of the most skillful players I’ve seen on a football field.
“He is a massive signing for the club and look forward to seeing him in Titans colours.”