Some 200 Britons were on board the Viking Sky ship which sent a mayday call after losing engine power, prompting the start of an operation to airlift 1,300 passengers and crew from the vessel in high winds.
Police in Moere og Romsdal said the ship’s crew had managed to anchor in Hustadvika Bay, amid fears the vessel would run aground.
A spokeswoman for Viking Cruises said the ship was safely travelling to the city of Molde, on Norway’s west coast, at 10am local time on Sunday under its own power.
There are still 436 guests and 458 crew members on board following the end of the evacuation, the operator said.
Some 479 passengers who were airlifted from the vessel are back on shore with the first due to fly home on Sunday.
Viking Cruises said 20 people suffered injuries, receiving treatment in Norway, with some already discharged.
A statement said: “Throughout all of this, our first priority was for the safety and wellbeing of our passengers and our crew.”
The operator’s chairman Torstein Hagen told Norway’s VG newspaper the events were “some of the worst I have been involved in, but now it looks like it’s going well in the end and that we’ve been lucky”.
The shipping tycoon, who is one of Norway’s richest men, added: “I am very proud of our crew.”
Footage online appeared to show the ship rocking dramatically, with debris falling from the ceiling and furniture including chairs sliding across the floor as passengers sat waiting to be rescued.
Derek and Esther Browne, from Hampshire, said the “whole boat was swaying, it was very rough” before they were airlifted to safety.
Mr Browne told BBC Radio 5 Live’s Stephen Nolan: “We had a few people on stretchers, several with cuts, two with broken limbs, but fortunately we were alright. We were airlifted onto the helicopter which was quite a frightening experience.”
He added: “I’d never been in a helicopter before, there were a lot of high winds, hovering overhead and the winchman came down and we were then collected up and so I shut my eyes as we arrived into the helicopter and there were 15 of us for about a 20-minute ride.”
Norwegian media said the majority of the cruise ship passengers were British and American tourists.
The ship was due to arrive in Tilbury in Essex on Tuesday.
Viking Cruises advised anyone with concerns about guests who were onboard to visit the Viking Cruises website.
The 745ft Viking Sky was built in 2017 and is described on the official website as a “comfortable, award-winning ship, intimate and thoughtfully created by experienced nautical architects and designers to enrich your interaction with your destination in every way”.
A spokeswoman for the Foreign Office said: “We are in touch with Norwegian authorities and stand ready to help any British people who require our assistance”.