The 41-year-old replaces Massimiliano Allegri who was sacked after a fifth-place finish last season, as the club aims to overhaul its operations.
No official details were immediately announced, but Italian media said Amorim, 41, had signed a two-year contract.
"I know exactly what this Club means: history, prestige and an extraordinary fanbase around the world. It is a challenge I embrace with pride and enthusiasm, fully aware of what these colours represent," Amorim said in a statement.
"I can't wait to get started and to experience every day the passion that drives AC Milan."
Milan concluded an abysmal second half of the season with a 2-1 home defeat by Cagliari on the last matchday, winning just one of their final four matches. The final whistle was met with heavy booing from the San Siro fans as they missed out on a place in Europe's top competition for a second season in a row.
Amorim had a difficult 14-month spell while he was head coach at Manchester United, defined by public barbs, stubborn tactics and poor form.
In October last year, United co-owner Jim Ratcliffe described Amorim as an "outstanding young manager" who needed three more years to prove himself, but over time that faith slipped and the Portuguese was sacked in January.
Amorim’s stock remains high on the back of his achievements at Sporting CP, where the former Portugal midfielder guided the club to a first Primeira Liga title in 19 years in 2021 before capturing a second league crown in 2024.
Amorim, who won 14 caps for his country, is Milan's fourth managerial appointment since the club last lifted the Serie A trophy under Stefano Pioli in 2022.
A new brand of football
His first task will be to restore structure and belief to a squad that appeared short of both during the closing months of the campaign when Milan's attacking threat faded.
Amorim will be expected to move the team away from Allegri's cautious, risk-averse approach towards a more aggressive, entertaining brand of football.
"Ruben believes in high-press attacking football with quick transitions that enable greater goalscoring," the club's American Italian owner Gerry Cardinale said in a statement.
"His philosophy aligns perfectly with our vision, while his leadership qualities and track record in developing players stood out to us. We believe in Ruben and are excited to welcome him to the club."
The Portuguese coach will also need to win over a fanbase frustrated by the club's struggles since the 2022 title triumph.
Supporters made their anger clear after the Cagliari loss, hanging banners outside Cardinale's hotel and at San Siro with the message: "Go home: shame on you," after Milan had to settle for a place in the second-tier Europa League competition.
Looking ahead to another season without Champions League football, Milan face a difficult transfer window as they try to keep key players while reshaping a squad that fell short.