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The designs by the two studios beat six others in a competition launched earlier this year.
"The purpose of the contest was to come up with a proposal that can be the starting point for the artistic design of the new banknote series and conveys the theme The Sea in a good way," said a translated statement from the bank.
Snøhetta's theme for the designs was The Beauty of Boundaries, which celebrates landmarks along Norway's vast coastline. These have been abstracted and pixellated to create patterns of coloured blocks in different shades.
"The beauty of boundaries is about the transition between sea and land, where something meaningful and interesting happens," said Snøhetta.
A different colour dominates each note: from green used on the 50 kroner design through red, blue and orange, up to purple on the 1,000 kroner note.
In Snøhetta's competition entry, the front design of the notes were largely covered by black-and-white photographs of nautical scenes, with subtle coloured strips overlaid.
These were dropped by the bank for The Metric System's illustrations of traditional and contemporary sailing vessels, seascapes and marine life.
"The front pages of The Metric System is very well adapted to incorporate the necessary safety items," said the statement. "The expression is open, bright and typical Nordic."
Norges Bank is now working with the designs to integrate the security elements required to make the notes machine-readable and to prevent counterfeiting, before they are released in 2017.
"The final papers will therefore deviate somewhat from the starting point as shown above," the bank said.
Designs submitted to the competition are now on display at the Grafill offices in Oslo, Rosenkrantzgate 21, until 26 October.
Snøhetta also designed the graphics for Oslo's bid to host the 2022 Winter Olympics, but the city withdrew its entry earlier this week.
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