The man is thought to have contracted the virus in Liberia before travelling to the US nearly two weeks ago.
More than 3,000 people have already died of Ebola in West Africa and a small number of US aid workers have recovered after being flown to the US.
Monitoring
“An individual travelling from Liberia has been diagnosed with Ebola in the United States,” Centers for Disease Control and Prevention Director Thomas Frieden told reporters on Tuesday.
According to Mr Frieden, the unnamed patient left Liberia on 19 September and arrived in the US the next day to visit relatives, without displaying any symptoms of the virus.
Symptoms of the virus became apparent on 24 September, and on 28 September he was admitted to a Texas hospital and put in isolation.
The disease, which is not contagious until symptoms appear, is spread via close contact with bodily fluids.
Aid workers who caught Ebola in West Africa have come back to the US for treatment but this is the first case of a patient developing the virus on US soil, says the BBC’s Alastair Leithead in Los Angeles.
A hospital official told reporters on Tuesday the facility already had procedures in place to deal with any such potential cases.
Preliminary information indicates that the unnamed patient, who was described as critically ill, was not involved in treating Ebola-infected patients while in Liberia.
Health officials are working to identify all people who came into contact with the unnamed patient while he was infectious.
Those people will then be monitored for 21 days to see if an Ebola-related fever develops.
According to Mr Frieden, it is possible a family member who came in direct contact with the patient may develop Ebola in the coming weeks.
But “the bottom line here is I have no doubt that we will control this importation, this case of Ebola, so it does not spread widely in this country,” he added. “We will stop it here.”
The World Health Organization (WHO) says more than 3,000 people have died of the virus so far, mostly in Liberia.
Earlier on Tuesday, the CDC said the Ebola virus seemed to be contained in Nigeria and Senegal, with no new cases reported there for almost a month.
It is the world’s most deadly outbreak of the virus