The Houston-born attacker progressed through Dortmund's youth ranks, making 58 appearances and scoring 19 goals for the club's U17 and U19 teams.
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He also helped the U19 side win back-to-back A-Junior Bundesliga West titles in 2023 and 2024.
Campbell made his senior debut for Dortmund during the 2024/25 season, featuring seven times across the Bundesliga, Champions League and DFB-Pokal.
"In Cole, we're signing another highly talented player who will be a tremendous asset to us with his exceptional pace and one-on-one ability," sporting director Christian Weber said.
"We've been pursuing him for quite some time and are delighted that he has chosen to join us."