Allardyce used his role to negotiate a deal worth £400,000 to represent a Far East firm and gave advice on how to get around rules regarding the transfer of players in England.
In England, third-party ownership is illegal but Allardyce claimed he could help businesses get around this and that it was common practice among football agents.
The former Sunderland manager spent just 67 days in the job and stepped down with mutual consent. His only game in charge, England won 1-0 against Slokavia in a World Cup qualifier.
An FA statement read: "He accepts he made a significant error of judgement and has apologised.
"This is not a decision that was taken lightly but the FA's priority is to protect the wider interests of the game and maintain the highest standards of conduct in football.
"The manager of the England men's senior team is a position which must demonstrate strong leadership and show respect for the integrity of the game at all times".
Steve Bruce, Eddie Howe and Alan Pardew have all been linked with the now vacant position.