The actor says he feels fine and currently has no symptoms, but has been isolated since he found out that he may have been exposed to the virus.
In a tweet he said: "This morning I tested positive for COVID-19. I feel ok, I have no symptoms so far but have been isolated since I found out about my possible exposure to the virus.
"Stay home people and be pragmatic. I will keep you updated on how I'm doing. No panic."
In an accompanying video, Elba says he was tested after he discovered a person he had recent contact with had tested positive for COVID-19.
He said he immediately self-isolated and got tested and had his results back today.
He also urged followers to think about social distancing and washing their hands, adding they should be vigilant to mitigate the spread of the virus.
"There are so many people whose lives have been affected, from those who have lost people they love, to people that don't even have it and have lost their livelihoods," he said.
"This is real."
The actor's announcement comes as Health Secretary Matt Hancock confirmed that 55 people had now died after testing positive for coronavirus,
Source: Sky News