The 26-year-old Dutch midfielder will join the Bundesliga side for the remainder of the 2023/24 season.
The deal comes on the first day of the 2024 winter transfer window, which remains open until February 1.
Van de Beek will be pushing for more playing time in Germany after making two appearances for United so far this season.
Eintracht Frankfurt are currently sixth in the Bundesliga and face a UEFA Europa Conference League play-off with Union Saint-Gilloise of Belgium in February.