This move comes after more than a decade of government planning and the government says it does not expect that any jobs will be affected.
The government has announced that FM stations in the country will begin to go silent from next week and the shutdown process will be complete by the end of 2017.
The country is switching from FM to digital radio (also known as DAB) because the digital options offers more channels, savings for broadcasters and better audio quality.
"The main reason that Norway is the first is because of the Norwegian landscape, which has deep fjords, high mountains and scattered communities," the government said in a statement. "This makes it particularly expensive to operate the Norwegian FM networks compared with other countries."
The Norwegian government estimates that radio stations will save more than $23.5 million a year by switching to the DAB format, allowing them to invest further in better radio content.
This move comes after more than a decade of government planning and the government says it does not expect that any jobs will be affected directly by the switch.
However, stakeholders and critics say the switch could leave 2 million cars without radio access - a potential safety hazard.
Other countries, such as the UK, are planning to make the switch so the success, or otherwise of this transition will be closely monitored.
Norway has a population of about 5.2 million people, 70% of which already have DAB radios, according to Radio.no, a website backed by the country's public broadcaster.