The exemption from entry restrictions will apply to persons residing in Sweden and Finland who commute to Norway by day.
The commuters will be tested every seven days for covid-19.
The message comes after Prime Minister Stefan Löfven's conversation with Erna Solberg on Friday.
"We agree that the situation for the Swedish border commuters is difficult and that it must be resolved," says Stefan Löfven in a written comment to TT.
It was on 28 January that the Norwegians closed the border with Sweden to prevent the spread of infection.
The result was that thousands of Swedes, were by a large number of Värmlanders, who work in Norway could no longer go to work.
In one fell swoop, both pay and social security networks disappeared.
"People should not be left without income because they are prevented from getting to their jobs," writes Löfven.
The text is updated