The Pioneering Spirit, owned by Allseas, used its vast lifting capacity for the first time to remove a platform for scrappage.
It carried out the operation on Monday, and is taking the platform to a Norwegian yard.
The ship's first lift was in the Norwegian sector of the North Sea.
After the fitting of additional lifting equipment in the Netherlands, the ship is booked later this year to start work on platforms in the UK North Sea.
Its arrival begins to open up the market for scrapping ageing North Sea equipment, which is estimated as being worth around Â£40bn in the next four decades.
The Pioneering Spirit was built in Singapore and fitted out in Rotterdam.
It is also capable of lifting the steel jackets on which platforms have been sitting since the 1970s.
One of the world's biggest ships has begun a new era for the North Sea oil and gas industry.