Critics have warned it is both risky and unpopular, not least because an estimated two million cars on Norwegian roads are not equipped with DAB receivers.
There are also fears that elderly and vulnerable people, often cut off by fjords and mountains, may be left unable to receive emergency warnings - traditionally broadcast on FM.
A poll by a national newspaper in December found that 66% of Norwegians were opposed to the switchover, and only 17% were in favour.
The change is being pushed through regardless, and the northern city of Bodoe will be first to go DAB-only on Wednesday.
Critics are urging Norway's government to change their tune as digital radio adapters are expensive
Norway's parliament voted in favour of switching off FM radio after hearing it would lead to a greater choice of radio stations, as well as clearer sound.
But Ib Thomsen, an MP from the Progress Party, said: "We are simply not ready for this yet.
"There are two million cars on Norwegian roads that don't have DAB receivers, and millions of radios in Norwegian homes will stop working when the FM network is switched off. So there is definitely a safety concern."
Ole Joergen, head of Digital Radio Norway, has admitted that cars will be the "biggest challenge" because a good digital adapter for an FM car radio costs about 1,500 Norwegian crowns (£142).
Other countries will be watching with great interest, with Switzerland planning to retire its FM network in 2020.
The UK government says it will consider a switchover once 50% of listeners are using a digital radio - a milestone which analysts say could be reached by the end of this year.