It follows reports that President Trump was outraged by comments made by Mulvaney during the Ukraine corruption saga.
The allegations of abuse of power over the Ukraine incident led to impeachment proceedings against President Trump.
Mulvaney's departure has been on the cards for the last few weeks.
Mr Mulvaney is to become US special envoy to Northern Ireland, while North Carolina lawmaker Mark Meadows has been appointed to take over his former position.


Trump says US, Israel to hold off on fresh Iran attack in hope of quick deal
Israeli strikes kill two in Gaza, destroy medicine storage warehouses
Thirteen die in tourist plane crash over Peru's Nazca Lines
Bomb carried by woman kills three, injures 21 near Moscow restaurant, authorities say
