The White House said Mr Trump’s expected stay of “a few days” at Walter Reed National Military Medical Centre was precautionary and that he would continue to work from the hospital’s presidential suite.
He walked out of the White House on Friday evening wearing a mask and gave a thumbs-up to reporters but did not speak before boarding Marine One.
Members of the aircrew, Secret Service agents and White House staff wore face coverings to protect themselves from the president onboard the helicopter.
In a video message recorded before leaving for Walter Reed, Mr Trump said: “I think I’m doing very well, but we’re going to make sure that things work out.”
“Going well, I think! Thank you to all. LOVE!!!” he wrote in his first tweet from the hospital on Friday night.
Just a month before the presidential election, Mr Trump’s revelation that he was positive for the virus came via an early morning tweet after he had returned from an afternoon political fundraiser.
He had gone ahead, saying nothing to the crowd though knowing he had been exposed to an aide with the disease that has infected millions in America and killed more than a million people worldwide.
First lady Melania Trump also tested positive, the president said, and several others in the White House have too, prompting concern that the White House or even Mr Trump himself might have spread the virus further.
Several administration officials pointed to the Rose Garden announcement of Mr Trump’s nomination of Judge Amy Coney Barrett to the Supreme Court as the possible connection between cases that spanned Washington on Friday.
Former White House counsellor Kellyanne Conway, the president of the University of Notre Dame, and at least two Republican senators who were also present at the event – Mike Lee and Thom Tillis – announced on Friday they had tested positive and were isolating.
Mr Trump’s campaign manager, Bill Stepien, has also tested positive for the coronavirus and is experiencing “mild flu-like symptoms”.
Mr Trump’s immediate campaign events were all cancelled, and his next debate with Democrat Joe Biden, scheduled for October 15, is now in question.
Tonight I tested positive for COVID-19. My symptoms are mild (light cough) and I’m feeling fine. I have begun a quarantine process in consultation with physicians.
As always, my heart is with everyone affected by this global pandemic. ❤️
— Kellyanne Conway (@KellyannePolls) October 3, 2020
The president’s physician Sean Conley said Mr Trump was given an experimental antibody combination which is currently in clinical trials before attending hospital.
He added the president “remains fatigued but in good spirits” and that a team of experts was evaluating both the president and first lady in regard to next steps.
Late on Friday, Dr Conley issued an update that said Mr Trump is “doing very well” and is “not requiring any supplemental oxygen”.
But he said that, “in consultation with specialists we have elected to initiate Remdesivir therapy,” an antiviral medication.
The first lady, who is 50, has a “mild cough and headache,” Dr Conley reported, and the remainder of the first family, including the Trumps’ son Barron, who lives at the White House, tested negative.