The 22-year-old right-back joins the Premier League side for an undisclosed fee after completing a medical.
Hunt came through the youth ranks at Huddersfield and has gone on to make 110 league appearances for the first team.
His performances last season alerted Ian Holloway to his potential and he has swooped to make him the 12th new signing at Selhurst Park since Palace won promotion to the English top flight.
Hunt admitted that he was sad to leave but was relishing the chance to test himself at the highest level.
"They (Huddersfield) showed incredible faith and trust in me and have played a massive part in starting my career," he told Huddersfield's official website. "I would also like to thank all Huddersfield Town fans.
"As a young player, they really helped me settle into the team – right from my full debut at Arsenal and ever since.
"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."
