The Ghanaian left-back, 17, is a senior player with the Accra Lions and has been trialling with Barca after impressing at Chelsea.
He spent three weeks with Chelsea before arriving at Barca on Friday. He is currently training with the Juvenil B team.
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Oduro's advisor, Vinyl Tong, told Sport: "Due to his profile and characteristics, he is reminiscent of Alphonso Davies. Powerful in duels, a born finisher, with great driving ability, breaking lines...he will come out for sure this summer, he needs to make the leap.
"At Chelsea they ended up very happy with him."