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 adds seven countries to full travel ban list
US President Donald Trump has expanded a list of countries subject to a full travel ban on Tuesday, prohibiting citizens from an additional seven countries, including passports from Syria and Palestine, from entering the United States.
Family of alleged Bondi gunman unaware of 'radical mindset', say Indian police
The alleged gunman shot dead by police during Sunday's attack on Australia's Bondi beach was originally from the southern Indian city of Hyderabad and his family did not know about his 'radical mindset', Indian police said on Tuesday.
Trump orders 'blockade' of sanctioned oil tankers leaving, entering Venezuela
US President Donald Trump has ordered on Tuesday a "blockade" of all sanctioned oil tankers entering and leaving Venezuela, in Washington's latest move to increase pressure on Nicolas Maduro's government, targeting its main source of income.
Israeli forces kill Palestinian teen in West Bank, health ministry says
The Israeli military have shot dead a 16-year-old Palestinian during a raid on the town of Tuqu' on Monday, the Palestinian health ministry said, the latest deadly incident in a recent surge of violence in the Israeli-occupied West Bank.
Trump sues BBC for defamation, seeks up to $10 billion in damages
US President Donald Trump has sued the BBC on Monday for defamation over edited clips of a speech that made it appear he directed supporters to storm the US Capitol, opening an international front in his fight against media coverage he deems untrue or unfair.
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