The forward has signed a contract until 2027 and will wear the number 26 jersey at the 13-time Greek champions.
Financial details of the transfer were not disclosed by the club but British media reported that the former France international will earn 2.5 million pounds ($3.32 million) per season, making him one of AEK's highest earners.
Martial scored 90 goals in 317 games in all competitions for United, helping them win the Europa League, the FA Cup and two League Cups. His last appearance for the club was in December after being sidelined by frequent injuries over the years.
AEK, who also signed former Tottenham Hotspur and Sevilla midfielder Erik Lamela in the close season, are top of Super League Greece with 10 points from four matches ahead of visiting Kallithea on Sunday.