Premier League shareholders voted unanimously on Thursday in favour of Barber representing the League for the third season since Albion were promoted in 2017.
Chairman Tony Bloom said: “We are extremely proud that Paul has again been elected to these prestigious positions in English football for the third successive season.
“It reaffirms his professional standing among the other Premier League clubs and demonstrates their faith in his ability and understanding of the game.”
Barber said: “It’s an honour to be re-elected to represent the clubs in the Premier League and I look forward to serving on both the FA Council and PGB in the season ahead.”