Thanking Tillerson for his service on Twitter, Trump said the new state secretary would do "a fantastic job".
Tillerson, a former chief executive of ExxonMobil, was only appointed to the job just over a year ago.
The president also nominated Gina Haspel to become the first woman director of the CIA.
A senior White House official told the BBC about the timing of the announcement: "The president wanted to make sure to have his new team in place in advance of the upcoming talks with North Korea and various ongoing trade negotiations."
Tillerson was on an official tour of Africa last week when he was apparently caught unawares by Trump's announcement that he would hold talks with North Korean leader Kim Jong-un.
The top US diplomat's team said he was feeling unwell on Saturday and later in the weekend the state department said he would cut short his tour by a day.
On Monday, Tillerson appeared to depart from White House talking points when he backed British authorities in blaming the Kremlin for the poisoning of a former Russian spy near his home in southern England.
The secretary of state said the nerve agent attack "clearly came from Russia" and "certainly will trigger a response".
But earlier in the day the White House declined to point the finger at Russia.
Reports have swirled of a schism in the Trump administration between the commander-in-chief and his top diplomat, as the US faces a host of vexatious foreign policy conundrums, from North Korea to Iran.
Last October Tillerson was forced to convene a news conference to deny reports that he was considering quitting, though he did not comment on a report that he had called his boss a moron after a meeting last July at the Pentagon.
Last autumn, Trump publicly undercut the former Texas oilman by tweeting that he was "wasting his time" trying to negotiate with nuclear-armed North Korea.
Tillerson was reported to be astonished at how little Trump grasped the basics of foreign policy.
The New York Times quoted sources as saying Trump was irritated by Tillerson's body language during meetings.
Tillerson was said to roll his eyes or slouch when he disagreed with the decisions of his boss.