Mr. Trump released a statement saying he was "proud" to nominate Pompeo to replace Tillerson.
Unlike Tillerson, a former businessman who lacked government experience when Trump picked him a year ago as secretary of state, Pompeo is well aware of the ways of Washington.
According to the Associated Press, White House chief of staff John Kelly called Mr Tillerson on Friday and advised him to watch out for a presidential tweet about him.
Last week Tillerson said that an upcoming meeting between Trump and Kim would focus on "talks" rather than "negotiations". "President Trump has demonstrated yet again that he is the Commander-in-Chaos", said Sen. "When you look at the Iran deal: I think it's awful, I guess he thinks it was OK". Golstein said that Tillerson had "every intention of staying". The official spoke on condition of anonymity because the official was not authorized to speak publicly.
Mr. Trump made Tuesday's move while Mr. Tillerson, formerly the CEO of ExxonMobil, was out of the country, finishing a week-long tour of several African nations.
The official said Trump wanted Pompeo in place before the US president's planned talks with North Korean leader Kim Jong Un and trade negotiations.
Mr Tillerson had no diplomatic or political experience before becoming secretary of state. Yet the president appears to expect a deal with Kim on denuclearization.
There was the usual clutch of polite, smarmy statements from all sides, but the sacking of Tillerson was abrupt and humiliating, redolent of Trump's reality TV style famously showcased in The Apprentice.
Mike Dubke, White House communications director, resigned later in May after months of chaos in the press shop. During that meeting Trump had called for an increase in America's nuclear weapons stockpiles in contravention of worldwide treaties.
Montella expets Sevilla to 'suffer' against Man United at Old Trafford
To reach those lofty heights, however, his team will likely have to perform better than they did three weeks ago in Seville. But Mata reckons the Red Devils can overcome their rivals to win the competition just as his Chelsea side did in 2012.
In December Mr Tillerson had offered to begin direct talks with North Korea without pre-conditions, backing away from a key U.S. demand that Pyongyang must first accept that any negotiations would be about giving up its nuclear arsenal.
Mr Tillerson was reported to be astonished at how little Mr Trump grasped the basics of foreign policy.
"The Secretary did not speak to the President and is unaware of the reason" he was sacked, said Steve Goldstein, under secretary of state for public diplomacy and Public Affairs in a statement to ABC News.
"Save your energy Rex, we'll do what has to be done!"
Early in 2018, Trump said on Twitter that Mr Tillerson was "wasting his time" trying to negotiate with North Korea.Tillerson had joined Defense Secretary Jim Mattis in pressing a sceptical Mr Trump to stick with the agreement with Iran and other world powers over Tehran's nuclear ambitions and he has taken a more hawkish view than Mr Trump on Russian Federation. Qatar calls these charges baseless. While Tillerson has in many ways rolled back the State Department's global presence and centralized its decision-making, Pompeo has empowered Central Intelligence Agency staffers.
Tillerson leaves behind a short-lived and mixed legacy at the State Department, where he sometimes ran afoul of the White House and stoked criticism for his handling of the department.
Calling your boss a "moron" is never a good sign.
Potential talks with North Korea were apparently the catalyst for booting Rex Tillerson from the State Department.