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.
Netanyahu orders deeper Israeli incursion into Lebanon
Israeli Prime Minister Benjamin Netanyahu said on Sunday he had ordered troops to move further into Lebanon in the battle against Hezbollah, despite a ceasefire announced more than six weeks ago.
US military says it turned away blockade runner trying to reach Iranian port
The US military has announced that it fired a missile into the engine room of a vessel trying to get through the US blockade of Iran on Friday.
Illegal mine collapses in China, killing five just days after Shanxi disaster
A mine shaft collapse during an illegal mining operation in China's southwestern Yunnan province killed five people and injured one, state media reported, days after the country's deadliest mining accident since 2009 left at least 82 dead.
Israel troops capture Beaufort Castle in southern Lebanon push against Hezbollah
Israeli troops have seized the 900-year-old Beaufort Castle and its strategic ridge in southern Lebanon, the military said on Sunday, a major advance against Hezbollah despite a ceasefire announced more than six weeks ago.
Jubilant PSG supporters spill onto Paris streets, some clash with police
Paris police deployed thousands of officers to control crowds at some of the city's hot spots, using teargas and arresting dozens following the win of the city's football club Paris St Germain in Saturday's Champions League final.
