The 21-year-old Germany youth international, who was a transfer target for several top European clubs, signed a deal at Dortmund to 2022.
"Mo Dahoud is a hugely talented and exciting player in the central midfield position whom we have been watching intensively for several years," said Dortmund sports director Michael Zorc.
"He has already proven he can play at top level."
Dahoud has scored six goals in 52 league appearances for Gladbach after rising through the Foals' youth ranks. He has also played in the Champions League and Europa League in the past few seasons.
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Dortmund are third in the Bundesliga and are through to the German Cup last four and the Champions League quarter-finals.
(Reporting by Karolos Grohmann; Editing by Alison Williams)
