The Australia international only signed a permanent deal with Brighton in January after making an initial loan move from Championship side Huddersfield Town.
Brighton announced that the 29 year-old is on the move again, ending a short spell with the Premier League club.
Seagulls head coach Graham Potter said: "Aaron has been an excellent professional during his time with us. From day one with us he fitted in really well.
"It's a good move for all parties. We have a number of really good players in that position and therefore Aaron goes with our blessing.
"I have really enjoyed working with him, and on behalf of everyone at the club I would like to thank him for his contribution and wish him well for the future."
Mooy made 32 appearances for Brighton last season, scoring twice and providing two assists.