The campaign is the first from Hometown London, which picked up the business in October.
It shows a series of quick images of people taking part in fun activities while on holiday, such as jumping into water, dancing and drinking. The film ends with the copy: "Where extraordinary happens."
The work has been created by Neda Shadanlou, who handled art direction, and Gemma Fowler, who took charge of copywriting. The media agency was Mindshare.
The campaign will run across TV, radio, print, digital and social media. The company will also relaunch its website.
Tamara Strauss, the director of marketing and PR at Royal Caribbean International, said: "We’re passionate about the holiday experience we sell and with this ambitious new marketing positioning, we will show guests just how truly mind blowing a Royal Caribbean holiday is.
"Nobody wants a holiday that is just ok, we want our guests to have an extraordinary experience while letting go of their everyday responsibilities.
"As part of this we want to honour our tradition of innovation which is exemplified through the range of experiences we offer at sea, from ice skating to surfing simulators onboard as well as virtual balconies in our staterooms."
Royal Caribbean International shifted its UK ad account into Hometown London just six months after hiring TBWA\London.