But he says his day-to-day priority remains his role as deputy chairman and chief executive at Albion.
Barber has been appointed a non-executive director at the A-League club in which Albion chairman Tony Bloom made an investment in March.
Since then, Barber has been working with Melbourne Victory managing director Caroline Carnegie on what is described as “a knowledge-sharing relationship to help benefit both clubs”.
In a statement, Barber said: “This is an opportunity for both clubs to explore opportunities of how we can work together to achieve our own individual ambitions on and off the pitch.
“My day-to-day priority will always be Brighton and Hove Albion, but this is an opportunity for us to share best practice in multiple sporting and administrative departments across the two clubs — while also representing Tony’s interests at Melbourne Victory.”
Barber becomes the first British football executive to serve in board level roles in the Premier League, EFL Championship, MLS and USL in North America, and A-League down under.
He has also worked for The FA and senior England teams at the both European Championships and World Cups.