The Australian international has signed a three-and-a-half year contract, after impressing during an initial loan spell during the first half of the season.
Mooy, who will be 30 in September, scored his second goal of the season for Brighton during the painful 3-1 loss at Bournemouth last Tuesday.
He signed a three-year contract at Huddersfield prior his loan switch to the Amex and Albion are believed to have paid a hefty loan fee to secure his services.
Reports suggest an offer in the region of £5m sealed his January deal for the player who joined the West Yorkshire team in June 2017 for £10m from Manchester City.
Head coach Graham Potter said, “We are delighted to have agreed a permanent deal with Aaron and Huddersfield. He’s been an important player for us and will have a key part to play going forward.
“We knew what Aaron would bring, and he’s proved to be an excellent addition to our squad and a great professional both on and off the pitch.”
Mooy was born in Sydney, and initially moved to England and Bolton Wanderers in 2006, joining their academy as a teenager. After two years with Bolton, at 18 he left to join SPL side StMirren, to play senior football.
After two seasons in Scotland, a four-year spell back in Australia followed. That saw stints with Western Sydney Wanderers and Manchester City’s sister club Melbourne City.
His form at the latter saw him win the Australian PFA Player of the Year. That prompted a move to England and to the Etihad to join City in 2016.
He was immediately loaned to Huddersfield, and in his first season helped the Terriers win promotion to the Premier League — alongside Albion — and was named in the PFA and EFL Championship teams of the season.
That prompted Huddersfield to make the move permanent, and Mooy was Town’s standout performer during their two-year stay in the top flight.