The former New Zealand half-back has been granted an early release from his contract by the Giants, prompting speculation that he could return to Bradford, the club where he made his name in the early days of Super League.
Huddersfield managing director Richard Thewlis said: "Robbie has a wonderful opportunity elsewhere that, as I see it, is too good for him to refuse and he leaves with my very best wishes for the future."
Hunter-Paul, 37, who took up his backroom role at the John Smith's Stadium two years ago after ending his playing career, said: "It's with some sadness that I leave.
"I have to thank everyone throughout the club for helping me have such a wonderful time when I came back after finishing playing."
- Sports & Recreation