The step was agreed by partners in Norway's new three-party coalition government during negotiations over the terms of their collaboration last week.
The industry will be completely phased out in accordance with the agreement, reports news agency NTB.
Animal protection charity Anima said it welcomed the development.
“This is a fantastic victory for the fight to stop the fur industry in Europe,” head of campaign Thorbjørn Schiønning said in a press statement.
Norway's Liberal (Venstre) party, the new and smallest partner in the three-way coalition, is credited with seeing through the initiative.
But Minister for Agriculture Jon Georg Dal of the populist Progress Party called the decision a setback.
“My job will now be to implement this in a way that ensures fur farmers receive sufficient compensation in the phasing-out period,” the minister said.
The Norwegian ban comes after a long-standing debate over the issue in the Scandinavian country.
In 2015, Norwegian fur farmers denounced a government proposal to slash financial support to the controversial industry, warning that it could lead to farm closures in vulnerable rural areas.
Some of Europe's largest anti-fur demonstrations have also taken place in the country.