The France international has signed for the 13-times Greek champions on a free transfer and will earn £2.5 million per season, making him one of AEK's highest earners, media reports said.
In an Instagram post, AEK welcomed Martial who has won the Europa League and an FA Cup title at United, scoring 63 Premier League goals for the club in 209 appearances.
AEK, who also signed former Tottenham Hotspur and Sevilla midfielder Erik Lamela in the summer, are top of Super League Greece with 10 points from four matches ahead of visiting Kallithea on Sunday.