The Republic of Ireland midfielder, 22, has joined Preston North End for undisclosed terms on a contract which runs until the summer of 2029.
Moran made three first-team appearances for the club after graduating from the academy.
He had been attracting interest since returning from his MLS loan with LAFC, with Portsmouth among the clubs tracking him.
Albion sporting director Jason Ayto said: “Andrew is another success story for the academy, progressing through the ranks before having good loans in the Championship and MLS.
“The next step for him is to establish himself somewhere and, with that in mind, a permanent transfer suits all parties. We wish him the best of luck for the future.”
Moran has previously played in the Championship for Blackburn and Stoke.
He featured for Albion in pre-season games in Marbella last summer and was said by head coach Fabian Hurzeler to have been close to earning a place in the Premier League squad
Preston are currently three points off a play-off place.
Their boss Paul Heckingbottom said: “Andy is someone we've been speaking to for a bit in the window.
“We’re delighted to have got another one who is our player, a young player, who has competed in the Championship and is a full international.
“He’s a good age, so it's a really good signing, not only for now for the club, but what we want to do going forward as well.”