According to MANA, the deal worth around £25m ($33m) comes with the option for two more ships.
The vessels will come with wave piercing bows.
The first 140-metre vessel is scheduled for delivery in July 2018 while the second is due in July 2019.
“The ships about to take shape in the docks of Kleven will be striking. They will attract interest to both the Norwegian ship building industry and to Hurtigruten as a leading player within the field of explorer tourism," said Hurtigruten chief executive Daniel Skjeldam.
The contract will be a welcome addition to Rolls-Royce's marine division which has been experiencing challenging times amid the global shipping downturn.
It reported a 16% fall in underlying revenue for its marine segment in 2015 to £1.3bn versus a year ago.
In October 2015, the company announced plans to cut 400 jobs in its marine business, in addition to the 600 job cuts it announced earlier in the year, bringing total job losses to 1,000.
In November 2015, the group was also considering a sale of all or part of its marine power and engineering business to focus on its aerospace and defence divisions, which form the bulk of the group’s revenue and profit.