Donald Trump will sign the executive order approving the temporary ban this evening.
The ban was an important part of his election campaign – despite outrage when he called for a "total and complete" shutdown.
The new order will also take away federal funding from "sanctuary cities" – except for the cities' police department.
Donald Trump has ordered a temporary ban of refugees entering the USA from Muslim countries
Mr Trump said in December 2015: "Donald J. Trump is calling for a total and complete shutdown of Muslims entering the United States until our country's representatives can figure out what is going on."
Donald Trump has temporarily banned refugees arriving in the USA from Muslim countries
He said the following month: "Look, we have to stop with political correctness. We have to get down to creating a country that's not going to have the kind of problems that we've had with people flying planes into the World Trade Centers, with the — with the shootings in California, with all the problems all over the world. We have to find out what's going on."
He later said: "It will be lifted, this [proposed] ban, when and as a nation we're in a position to properly and perfectly screen these people coming into our country."
Mr Trump is currently entertaining Prime Minister Theresa May in Washington. The pair are expected to give a joint press conference later this evening.
This is a breaking news story. More to follow…