Mr Trump's tweeted announcement came shortly after the White House press office had said Mr Bolton would shortly be giving a press conference on terrorism issues alongside Secretary of State Mike Pompeo.
Trump did not elaborate on what disagreements he had with Bolton.
Trump tweeted the news at about noon Tuesday. The President announced the plans for the meeting were canceled on Saturday.
Trump said he would name a new national security adviser next week.
The president and Bolton reportedly had clashed on North Korea and Afghanistan in recent weeks.
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Mr Bolton is a veteran and controversial figure closely linked to the invasion of Iraq and other aggressive foreign policy decisions.
"White House press secretary Stephanie Grisham told reporters: "[The president] didn't like a lot of his policies, they disagree".
Bolton, in response to Trump's tweet, said he offered his resignation Monday night. Bolton briefly considered running for president in 2016, in part to make the case against the isolationism that Trump would come to embody.
The president said he asked Bolton for his resignation Monday night.
It's unclear what candidates Trump is considering to replace Bolton.
Fox News host Brian Kilmeade broke news during the noon hour while guesting on Outnumbered as he revealed a text received by now-former National Security John Bolton.