All of the parties represented in parliament, with the exception of the small Christian Democrat party, agreed to back a proposal by the centre-left government for a "gender neutral" military conscription.
In practice, that means that Norway's mandatory one-year military service will be extended to women, probably as of 2015, according to the defence ministry's proposal.
"Norway will be the first European country to draft women in peacetime," a defence ministry spokesman, Lars Gjemble, said.
A number of other European countries have gone in the opposite direction in recent years, moving away from conscription towards professional armies.
Norway's parliament is expected to adopt the bill by a broad majority, but a date has yet to be set for the vote.
The move is seen as a step towards gender equality and a bid to diversify the competencies within the military.
It is not due to a lack of conscripts: only 8,000 to 10,000 Norwegians are called up each year, among the some 60,000 who are theoretically eligible.
The conscripts are selected based on physical and psychological tests, as well as their motivation.
"This is a historic day," Defence Minister Anne-Grete Stroem-Erichsen said.
"And it comes the very week when we are celebrating the 100th anniversary of women obtaining the right to vote," she added.
Norwegian women have been allowed to do military service on a volunteer basis since 1976. They currently represent about 10 percent of conscripts.
Even before the adoption of a "gender neutral" military service, the defence ministry had set a target of 20 percent women in the armed forces by 2020.
Outside of Europe, some countries such as Israel require both men and women to complete their military service.