The 24-year-old was released by his hometown club in a major clearout at the KC Stadium at the end of last season, having made his debut for the Airlie Birds at the age of 17.
He said: “This could be just the challenge I need at this stage of my career, and I’m excited about it.
“Obviously, it was disappointing to be told by Hull they were letting me go, because I love the club and the eight years there were fantastic.
“But, while it was sad to leave, it was great to know a club like Huddersfield were keen to take me on.”
Brown said: “At this stage of the year, it’s not easy to pick up a player of this quality, so we believe we’ve done exceptionally well to get him.
“For a player of his age to have played so many Super League games (101) proves he must have something going for him.
“And we’re now hoping this change of environment will be the catalyst to help Graeme reach his full potential.”