The president tweeted to thank General H.R. McMaster, saying he had done an “outstanding job & will always remain my friend”.
John Bolton, who has backed attacking North Korea and Iran, told Fox News his job would be to ensure the president has “the full range of options”.
The former UN ambassador becomes President Trump’s third national security chief in 14 months.
H.R. McMaster is the latest high-profile departure from the White House.
Last week, President Trump fired Secretary of State Rex Tillerson by a tweet, replacing him with former CIA Director Mike Pompeo.
John Bolton’s appointment does not require US Senate confirmation. He will take the job on April 9.
The National Security Adviser is the key counselor to the president on national security and foreign policy issues, and acts as a conduit for policy proposals coming from various government departments, including defense and state.
John Bolton, 69, said he was looking forward to working with President Trump and his team “to make our country safer at home and stronger abroad”.
He has been a foreign policy hawk in Republican circles for decades, having served in the administrations of Ronald Reagan, George H.W. Bush and George W. Bush.
President George W. Bush appointed John Bolton as US envoy to the UN, during which time diplomats privately criticized his style as abrasive.
A strident neo-conservative, John Bolton helped build the case that Saddam Hussein possessed weapons of mass destruction, which turned out to be wrong.
Known for his walrus moustache, John Bolton does not appear to have greatly moderated his views since his last spell in government.
John Bolton stands by the invasion of Iraq and has advocated in newspaper op-eds using military force against North Korea and Iran.
In a brief statement on March 22, General H.R. McMaster, 55, thanked President Trump for appointing him and said he was applying to retire from the US Army later this year.
The three-star general is leaving after just over a year as national security adviser.
The White House said President Trump and H.R. McMaster had “mutually agreed” that he would leave. He had been rumored for weeks to be on his way out.
His departure came a day after someone at the White House leaked to media that President Trump was advised this week in briefing documents not to congratulate Russian President Vladimir Putin on his recent re-election, but did it anyway.
General H.R. McMaster replaced Lt. Gen. Michael Flynn, who was fired after less than a month in the job for misleading the White House about his contacts with the Russian ambassador.
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