The 16-year-old striker has joined the Catalan club on a three-year deal and will play for Barcelona's U19 Juvenil A side this coming season.
According to reports, West Bromwich Albion will recoup a mere £235,000 in compensation for the teenager, who had been with the Baggies since he was six years old.
Born in Birmingham, Barry has played for both England and the Republic of Ireland at youth level. He has notably scored seven goals in nine games for England U16s.
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Barcelona stated that Barry "is considered as one of the best young players in English football."
Barry can play at centre forward and on the right wing.