The decision has been made as part of a shake-up instigated by David Moyes following his arrival from Everton as Sir Alex Ferguson's successor.
A former United player, Phelan came back to Old Trafford as a youth team coach in 1999, and was promoted to Sir Alex Ferguson's backroom team two years later, replacing Carlos Queiroz as assistant in 2008.
Steele was installed as goalkeeping coach in 2008 as replacement for Tony Coton, who was forced to retire due to injury.
Moyes said in a statement from the club: "I would like to put on record the club's thanks for everything Mike and Eric have done.
"I will be looking to appoint my own members of coaching staff at some point in the future, however, I'd like to take this opportunity to give them both our best wishes for their future careers."
Executive vice-chairman Ed Woodward said: "I'd like to thank Eric and Mick for the enormous contributions they have made to the success of Manchester United in their time here. Their professionalism, ability and diligence have been a credit to them.
"They are top class football men and everyone here wishes them well for long and successful careers in the game."
- Sports & Recreation
- Sir Alex Ferguson
- David Moyes
- Carlos Queiroz
- Tony Coton