Marine One arrived on the South Lawn of the White House around 5:20 p.m. and left with the president about 1 hour later. Trump walked to the helicopter under his own power.
White House press secretary Kayleigh McEnany said the president has experienced "mild symptoms" from the virus.
"Out of an abundance of caution, and act the recommendation of his physician and medical experts, the president will be working from the presidential offices at Walter Reed for the next few days," she said in a statement.
Earlier Friday, Trump's physician, Dr. Sean Conley, said he was treated with Regeneron, an experimental antibody treatment. He described the president as being in "good spirits," and said first lady Melania Trump, who also tested positive, had a mild cough and headache.
Around 6:30 p.m., the president tweeted a video of himself in the Oval Office offering an update.
"I want to thank everybody for the tremendous support. I'm going to Walter Reed hospital. I think I'm doing very well but we're going to make sure things work out. The first lady is doing very well, so thank you very much. I appreciate it. I will never forget. Thank you," he said.
Trump announced his and the first lady's coronavirus diagnoses late Thursday. They were tested shortly after it became known that Trump adviser Hope Hicks had tested positive for the coronavirus.
Both entered quarantine on Friday, they said.
White House chief of staff Mark Meadows told reporters Trump was experiencing "mild symptoms," is in "good spirits," energetic and is conducting "business as usual."
"We have a president that is not only on the job, he will remain on the job," Meadows said.
"His first question to me this morning is how is the economy doing? How are the [congressional] stimulus talks?"
"As too many Americans have done this year, [the president] and I are quarantining at home after testing positive for COVID-19," Melania Trump tweeted. "We are feeling good and I have postponed all upcoming engagements. Please be sure you are staying safe and we will all get through this together."
Vice President Mike Pence his wife, Karen Pence, tested negative for the coronavirus, his spokesman Devin O'Malley said Friday.
"Vice President Pence remains in good health and wishes the Trumps well in their recovery," O'Malley tweeted.
The Trumps' 14-year-old son Barron also tested negative, a White House spokesperson told USA Today.
The White House canceled most of the president's schedule for Friday, which had included a roundtable discussion with supporters at the Trump International Hotel in Washington and a campaign trip to central Florida.
The medical community notes that the president is at higher risk for severe COVID-19 and potential complications, given that he is 74 and is technically classified as "obese," according to his White House records.
People around the world reacted with sympathy and criticism Friday to the news.
Democratic presidential nominee Joe Biden, who participated in a debate with Trump on Tuesday in Cleveland, said he tested negative on Friday.
"I'm happy to report that Jill and I have tested negative for COVID," he tweeted. "Thank you to everyone for your messages of concern. I hope this serves as a reminder: wear a mask, keep social distance, and wash your hands."
Earlier, Biden said he hopes the president and first lady recover quickly.
"Jill and I send our thoughts to President Trump and first lady Melania Trump for a swift recovery," he tweeted. "We will continue to pray for the health and safety of the president and his family."
Many who posted on social media following the diagnosis also expressed personal concern and well-wishes.
"Karen and I send our love and prayers to our dear friends President [Trump] and [first lady] Melania Trump," Pence tweeted earlier. "We join millions across America praying for their full and swift recovery. God bless you President Trump and our wonderful first lady Melania."
"Wishing my friend [Donald Trump] and [the first lady] a quick recovery and good health," Indian Prime Minister Narendra Modi tweeted.
"Best wishes to President Trump and the First Lady," said British Prime Minister Boris Johnson, who recovered after being hospitalized in intensive care with COVID-19 earlier this year. "Hope they both have a speedy recovery from coronavirus."
"Like millions of Israelis, Sara and I are thinking of President Donald Trump and First Lady Melania Trump and wish our friends a full and speedy recovery," Israeli Prime Minister Benjamin Netanyahu tweeted.
Russian President Vladimir Putin offered support in a telegram to the White House.
"I am certain that your inherent vitality, good spirits and optimism will help you cope with this dangerous virus," he wrote.
Some of Trump's political opponents stepped back from partisan differences to express personal sympathy.
"We must all pray for the full recovery of the President and his wife," the Rev. Jesse Jackson Sr. tweeted. "For whatever religious or political persuasion you may be, we must all pray as millions of people are affected by this disease."
"I will keep the President and First Lady in my prayers, and I wish them a speedy recovery," added Rep. Ted Lieu, D-Calif.
Others called attention to Trump's frequent downplaying of the pandemic and his flouting of public health recommendations -- including those from his own administration -- by often refusing to wear a mask and holding indoor public rallies.
The president should have expected this outcome, critics said.
"He failed to protect the country. He couldn't even protect himself," George Conway of the Lincoln Project, a group of anti-Trump Republicans working against his re-election, tweeted.
"President Trump and the first lady have paid the price for his gamble to play down the COVID-19," Hu Xijin, editor-in-chief of Chinese state-owned newspaper The Global Times, tweeted.
Trump has repeatedly called COVID-19 the "China virus" and has blamed Beijing for the deadly outbreak, which has infected 34.3 million people and killed more than 1 million worldwide -- including 7.3 million cases and about 208,000 deaths in the United States, according to Johns Hopkins University.