"Mick is a very talented and professional coach, whose ability and contribution to the club's success has often been understated."
Former United stars Brian McClair and Laurent Blanc had also been linked with the vacant post.
Phelan has been working as a first team coach since 2001, the year Steve McClaren left to coach Middlesbrough.
He played more than 100 games in five years at United, earning a Premier League winners' medal in 1993.
The defensive midfielder, who also played occasionally at full-back, stayed with United for another year but didn't make enough appearances to warrant another medal and was omitted from the squad for the FA Cup final.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.