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.
"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.