And Fabian Hurzeler has highlighted the “really important” role he has played in their partnership over the last two years.
The clubs have agreed a compensation package to allow the Seagulls’ assistant head coach to join Roberto De Zerbi in North London.
Crofts starred for Albion as a midfielder, coached an under-23s side spearheaded by emerging striker Evan Ferguson and was then promoted to a first-team role.
He initially stepped up when Graham Potter and five colleagues suddenly left for Chelsea in 2022 and has since assisted both De Zerbi and Hurzeler.
Albion sporting director Mike Cave said: “Andrew has been a fantastic member of the coaching staff in both our men’s first team and the boys’ academy, adding a huge amount of value to every role he has undertaken.
“While we are disappointed to see him leave, we understand that this is a fresh opportunity for him to challenge himself in a new environment.
“He is a great example of the pathway at the club for both our players and staff. We wish him the best of luck for the future.”
Hurzeler added: “Crofty has been really important for me both on the training pitch and off it, given his strong connection to Brighton.
“The club has a well-known pathway for up-and-coming players, but he is a great example of the coaching pathway we have here too.
“It’s a credit to him that every time he has been presented with an opportunity he has taken it and I know that not only I, but also my coaching staff, have learnt a lot from him. I wish him good luck.”
Crofts made 125 appearances for Albion and rejoined as under-23s player-coach in 2019, going on to become the team’s head coach in succession to Simon Rusk.
He has also had a role on the coaching staff at the Wales national team.