Wright, who turns 38 next month, has claimed 567 wickets at 32.30 in a 196-match first-class career that has spanned 20 seasons. His best innings figures of 7 for 53 came against Gloucestershire at Bristol in 2021.
"I am delighted to be joining Sussex for the 2024 season and beyond," Wright said. "I have long admired the club and am looking forward to contributing to its future success.
"Speaking to Paul Farbrace [head coach] and having played against the team a number of times I am excited to be joining such a talented and ambitious group. Hopefully, I will take lots of wickets and provide some valuable experience to the team."
Farbrace added: "I'm delighted that Chris has committed the next two seasons to joining our project at Hove. He is a vastly experienced cricketer who will bring skill, experience, and a huge passion for the game.
"Chris is someone I have admired for a long time, and his quality with the ball will be fantastic for our developing team and will help us to win matches."
Sussex will be the fifth county of Wright's first-class career, following earlier stints at Essex and Middlesex, as well as a successful period at Warwickshire between 2011 and 2018, where he helped win the County Championship in 2012.