The 19-year-old winger has signed a contract until 2025 with BVB, which take the Dutchman on a free transfer.
BVB chief Sebastian Kehl said: "Jayden, whose development we have been closely monitoring for years, has shown in the past that he can be a difference player with his speed and talent.
"After more than a year out of injury, he will now need time to find his way back to his old strength and to fully establish himself in senior football. We want to give him this time and gently introduce him.
"If Jayden gets through the phase ahead and stays clear, we have a great talent on board in him."
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