Dembele, 18, a French youth international, has been impressive in his first full Ligue 1 season, scoring 12 goals in 25 matches.
"Ousmane can play in attack in almost every position," said Dortmund sports director Michael Zorc on Thursday. "He is powerful in one-on-one situations, can play with both feet and is quick and dangerous."
Dembele said the Bundesliga outfit had been watching him for a while.
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"Dortmund tried very hard to sign me and always kept very close contact," he said in a club statement. "I was impressed."
Dortmund, who are sure to finish second to champions Bayern Munich this season, host Cologne in their final game on Saturday.
They meet Bayern in the German Cup final on May 21.
(Reporting by Karolos Grohmann; Editing by Tony Jimenez)
