The Ghanaian 16-year-old was snapped up by the Red Devils on deadline day after impressing at the AEGON Future Cup and will join up with the club's academy squad.
Louis van Gaal has raided his former club to sign the teenager, who will join up with the Red Devils's Academy squad once the move has been officially rubber stamped.
The arrival of Fosu-Mensah caps a busy transfer deadline day for United which also saw Radamel Falcao and Daley Blind arrive at Old Trafford while Tom Cleverley, Danny Welbeck, Javier Hernandez, Nick Powell, Tom Lawrence and Michael Keane left the team.
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A statement read: "Manchester United agreed a deal to sign Timothy Fosu-Mensah from Ajax ahead of the transfer deadline.
"The 16-year-old is a powerful defender who caught the eye at the AEGON Future Cup and is highly regarded in his homeland.
"Fosu-Mensah still requires an International Transfer Certificate to be processed in order to make his debut for Paul McGuinness' Academy squad, but his versatility and ability mark him out as an excellent addition for the Reds."