The ban, which Mr Trump described as "unprecedented" will come into force at midnight on Friday, local time. US restrictions on people arriving in the US from China and Iran were already in place.
Mr Trump said the prohibitions would also "apply to the tremendous amount of trade and cargo," and "various other things as we get approval," but this was later clarified by the White House as being incorrect.
"This is the most aggressive and comprehensive effort to confront a foreign virus in modern history," he said.
More than 1,200 COVID-19 cases have been confirmed in the US, including 36 deaths.
Shortly after the address, the White House announced that Mr Trump, 73, would be cancelling a trip to Nevada and Colorado out of "caution".
On Thursday morning, the World Health Organization formally declared the outbreak a pandemic after it reached more than 100 countries.
Globally, as of Thursday midday, more than 125,000 cases of the virus had been confirmed.
Of these, approximately 68,000 had recovered and 4,628 had died.
Coronavirus symptoms can range from mild illness to pneumonia, according to the federal government's website, and can include a fever, coughing, sore throat, fatigue and shortness of breath.
People who believe they may have contracted the virus are advised to call their doctor before organising an appointment or contact the national Coronavirus Health Information Hotline on 1800 020 080.