The club's website has confirmed the 18-year-old will move to Old Trafford in January, subject to medical, personal terms and work permit.
Diallo made three appearances for Atalanta last season.
United have been scouting the Ivory Coast winger since 2016.
The fee for Diallo is €21m, plus €20m in add-ons.
We have reached an agreement with Atalanta for the future transfer of Amad Diallo, subject to a medical, personal terms and work permit. #MUFC
— Manchester United (@ManUtd) October 5, 2020