The 22-year-old arrives for an undisclosed fee and has signed a four-year contract with the Premier League new boys.
Speaking on his move to Selhurst Park, Hunt said: "I'd like to thank the chairman Dean Hoyle and the board of directors for everything during my time at the club."
He added on the club's official website: "If it wasn't for them I would have probably moved on after my loans away, but they showed incredible faith and trust in me and have played a massive part in starting my career.
"I've been at the club for a very long time and it will always hold a special place in my heart, but now I have an exciting new challenge to go and play Premier League football against some of the world's best players.
"I've made a lot of friends at Huddersfield Town in terms of players and coaches and I would like to thank them all too.
"With the chairman, Nigel Clibbens, Ross Wilson and the manager Mark Robins in charge, I believe the club's future is very bright."