The 39-year-old Portuguese, who will move to Old Trafford from Lisbon club Sporting on 11 November, has signed a contract until June 2027.
Former United striker Ruud van Nistelrooy, who took charge on an interim basis after Erik ten Hag was sacked on Monday, will stay on for the club’s next three fixtures.
Amorim is the sixth permanent manager United have appointed since Sir Alex Ferguson’s 26-year reign ended with his retirement in 2013.
In a statement, the club said that “Ruben is one of the most exciting and highly rated young coaches in European football.
Sporting confirmed in a statement that United have agreed to pay 11m euros (£9.25m) to trigger a release clause in Amorim’s contract.
Amorim’s first fixture in charge of the Red Devils is set be on 24 November, after the international break, in the Premier League against newly promoted Ipswich.
His first home game will be against Norwegian side Bodo/Glimt in the Europa League on 28 November, with a league game against Everton the following weekend.
United will announce who will be on Amorim’s coaching staff at a later date.
After losing against rivals Porto in the Portuguese Super Cup on 3 August, Amorim has guided the side he led to last season’s Primeira Liga title through a 14-game unbeaten run.
Amorim is due to be in the dugout on Friday when Sporting host Estrela in a league game (20:15 GMT).
Sporting are also at home in the Champions League on Tuesday when they play Manchester City.
Amorim’s last game in charge is set to be against former club Braga in the league on 10 November, before European top-flight football pauses for Nations League games.
Amorim inherits a Manchester United side that is 14th in the Premier League and 21st out of 36 teams in the Europa League table.
But the Portuguese coach arrives at Old Trafford with a reputation as one of Europe’s most promising managers.
The former Portugal midfielder started his managerial career with third-tier Casa Pia in 2018.
He joined Braga’s B team that summer and managed the side for just 11 matches until being appointed manager of the first team where he oversaw 13 games before Sporting made a move.
In his 13 matches in charge, Amorim inspired Braga to their first away win against Benfica in 65 years and victory in the Taca da Liga cup final – Portugal’s equivalent of the League Cup – against Porto.
His success with limited resources convinced Sporting to make Amorim the most expensive managerial hire in Portuguese history when they paid £8.5m to extract him from his contract at Braga.
Sporting’s gamble paid off as Amorim guided the club to the 2020-21 league title in his first season with the club.
It was their first in 19 years and they lost just once during the campaign, after the title had already been won.
Despite a number of high profile departures – including Manuel Ugarte to Paris St Germain – Amorim guided Sporting to a second league title in four years last season.
As part of his managerial training, Amorim spent time at Old Trafford in 2018 when the club was managed by compatriot Jose Mourinho.
He has often been compared to Mourinho, who has also coached at Real Madrid, Chelsea and Tottenham, and is currently at Fenerbahce.
Amorim met with representatives of West Ham United in April 2024 with a view to replacing David Moyes as manager.
He later apologised for the trip to London, saying it was “disrespectful” and “a mistake”.
Chelsea expressed interest in Amorim following Mauricio Pochettino’s departure at the end of last season, while Liverpool considered him as a successor for Jurgen Klopp before appointing Arne Slot.
