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.


Landslide at Guinea landfill kills 30, government says
Ukraine wants peace but won't give in, Zelenskyy says on Independence Day
New Zealand to introduce bill banning social media for children under 16
Ukrainian drone attack kills three in Russia's Krasnodar, officials say
Coach carrying German high-school students crashes in Netherlands
