The honour, presented by Italian newspaper Tuttosport, is given to the best player aged 21 and under that is based in Europe.
Spain international Gavi beat competition from some of Europe's most promising youngsters to land the award, including England and Borussia Dortmund midfielder Jude Bellingham, Real Madrid's Eduardo Camavinga and Bayern Munich's Jamal Musiala.
"I want to thank Tuttosport," Gavi said in a video message. "I want to thank my family, who are there in the good and bad times.
"I want to thank Barca, my teammates as without them this wouldn't be possible. It's an honour for me to get this award that any young player desires."
Gavi broke into Barca's first-team in July 2021. He made 47 appearances, scoring two goals for the Catalan club in all competitions last season.
He earned a call-up to the Spain national team and became the youngest player to represent La Roja at 17 years and 62 days and the youngest ever player to score for them at 17 years and 304 days.
Gavi has since won 12 caps for Spain and is a regular for club and country heading into next month's World Cup.
He recently signed a new contract with Barca that will keep him at the club until June 2026.