Eintracht have paid United a minimal loan fee and are covering the majority of Van de Beek's £125,000-aweek wages.
Eintracht have the option to buy Van de Beek, 26, for €11m (£9.55m), with €3m (£2.6m) in add-ons.
The move is the second loan for Van de Beek during his time at United after he spent a forgettable five months with Everton two years ago.
Van de Beek has played 62 times for United and scored only two goals.
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