"This will be his last day, but not really, because he will, always, be with us, helping all the way," Trump said in a post on Truth Social. "Elon is terrific!"
The president said the press conference will be held in the Oval Office on Friday.
Musk announced he was stepping down from his White House stint on Wednesday, giving Tesla investors some succour after shares slumped this year in part due to the backlash to his support of Trump and right-wing parties in Europe.
The billionaire spearheaded Trump's so-called Department of Government Efficiency(DOGE), charged with cutting federal spending.
On Tuesday, Musk criticised the price tag of Republicans' tax and budget legislation making its way through Congress.
In addition, he had recently pledged to spend less money on politics after he plunked down nearly $US300 million on Trump's presidential campaign and on other Republican candidates last year.
A former DOGE staffer said without Musk in the Trump administration, his cost-cutting Department of Government Efficiency project is likely to sputter out.
Software engineer Sahil Lavingia, who spent almost two months working for the group of pro-Musk technologists, said he expects DOGE to quickly "fizzle out."
"It'll just die a whimper," Lavingia, who was fired from DOGE earlier this month, told Reuters.
"So much of the appeal and allure was Elon."
He said he expected DOGE staffers to "just stop showing up to work. It's like kids joining a startup that will go out of business in four months."
That would cap a remarkable undoing for DOGE, which Musk initially vowed would cut $US2 trillion in federal spending. Instead, DOGE estimates its efforts have saved around $US175 billion so far and the group's tallies have been riddled with errors.
Lavingia, the 32-year-old founder and CEO of creator platform Gumroad, said he was recruited by DOGE through a personal contact and joined the team in March.
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