The 24-year-old has taken 112 wickets in 40 first-class games, while his useful lower-order batting has brought him four half-centuries, but he was released at the end of this summer.
Sussex's professional cricket manager Mark Robinson said: "Chris has got enormous potential. He can bowl genuinely quick and has the ability to be able to bat at six or seven, and is a natural athlete in the field."
Robinson added: "As yet, he hasn't been able to find the consistency needed to fulfil his potential. He is still young and we hope we can help Chris fulfil this rich promise and become not only a matchwinner at Sussex but also for England."