The 28-year-old has also signed a contract extension at Huddersfield, with his new deal running until 2022.
Australian international Mooy scored three goals in 29 Premier League appearances for the Terriers last season, also playing 90 minutes as Huddersfield were beaten by Derby County in their Championship opener on Monday.
“We are delighted to welcome Aaron to the club," Potter told the club's website. "He has played very well over the past two seasons in the Premier League, and will bring a different option and added competition to our midfield.
“He’s been a talisman for Huddersfield in recent seasons with his performances on the field; and he’s proved to be an excellent professional both on and off the pitch.
“I’m looking forward to working with him, and he is another good addition to our squad ahead of the new season.”
Mooy's initial loan spell at Huddersfield in 2016-17, when he joined from parent club Manchester City, was hugely productive.
He established himself as former manager David Wagner's key player in their promotion push, as they eventually beat Reading in the Championship Play-off final.
After two years in the Premier League he has now made more than 100 league appearances for the Terriers and, while his impact at top-flight level might not have lived up to some fans' hopes, it was unlikely the club would be able to keep hold of him following relegation.
His new contract suggests a belief in Jan Siewert's ability to take his side straight back up, but would also put the club in a stronger position should they have to sell in future.
He follows Adam Webster, Leandro Trossard, Neal Maupay and Matt Clarke as Brighton's fifth signing of the summer window.
The 26-year-old moves for an undisclosed fee after four years at Loftus Road, signing a reported three-year contract with the Owls.
Luongo has previously spent time with Swindon, Ipswich and Tottenham.