In a club statement on Friday, the Red Devils confirmed that Amorim will remain with Sporting Lisbon until November 11.
This means the 39-year-old’s first game in charge will be a Premier League trip to Ipswich Town.
Amorim has agreed a contract until June 2027, with the option of a further year.
United have paid Sporting an extra €1m (£840,000) in addition to his €10m (£8.4m) exit clause for an early release from his 30-day notice period.
He will replace Erik ten Hag, who was sacked on Monday, while Ruud van Nistelrooy will continue in an interim role until Amorim joins.
United’s next game is a league fixture at home against Chelsea on Sunday.
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