He wrote: 'Thank you to all my friends and followers for all the prayers and kind wishes. "I'm getting great care and feeling good".
Mr Biden will be sworn in as president on 20 January. It was widely believed the press conference was meant to take place at the Four Seasons Hotel in Philadelphia but Trump's team booked the gardening center by mistake.
Trump and many of his close associates have balked at public health officials' advice to wear masks and avoid crowds to stem transmission of the respiratory illness, which has roared to record levels in the United States as winter approaches.
On Sunday, it emerged that the Arizona state legislature would be closing for this week due to concerns over Covid-19.
Outgoing US President Donald Trump’s lawyer Rudy Giuliani was taken to hospital with COVID-19. Pic JUSTIN LANE EPA-EFE REX Shutterstock
The 76-year-old said he was "recovering quickly" in a tweet following his diagnosis on Sunday.
Chatfield said the Centers for Disease Control and Prevention, or CDC, guidelines would not consider them close contacts with anyone, even if Giuliani had been positive, but they want to go above and beyond in the interest of public safety with the recent spike in COVID cases nationwide. At all of the indoor events, Giuliani was frequently seen maskless and disregarding social-distancing guidelines as he shook hands with Trump supporters and posed for photographs with them. Several lawmakers who attended the unofficial hearing on November 30 also attended the Legislature's new member orientation later in the week, possibly exposing even more lawmakers and state government employees to the virus.
Giuliani was widely praised for his management of New York's response to 9/11 and was nicknamed "America's mayor" as a result.
Giuliani was also not experiencing virus symptoms at the time, according to Ellis.
The 76-year-old former NY mayor, hospitalized in Washington, had traveled extensively to battleground states to press Trump's quixotic effort to get legislators to overturn his election loss to Joe Biden and subvert the November vote.
Almost 14.6 million people have been infected with Covid-19 in the U.S., according to Johns Hopkins University, and 281,234 people have died - the highest figures of any country in the world.
The nation is nearing an average of 200,000 new Covid-19 cases per day, and it is thought a Thanksgiving surge is still to come.