Powered by liquefied natural gas (LNG), the ships are scheduled to be delivered in 2022 and 2024.
The ships, with an around 200,000 gross tonne capacity, will be built under a project named Icon.
Meyer Turku CEO Jan Meyer said: “Our partnership with RCL has created a number of groundbreaking ships such as Oasis, Celebrity Solstice, Quantum and Mein Schiff.
“We are grateful that Royal Caribbean engages with us in a new challenging journey to advance the state of maritime technology with a new class of cruise ships.
“Our common aim is to develop fuel cells to a level that allows their usage in a significant application to power the ship's hotel functions.”
The company noted that it would use the revenue generated from the new order to modernise the Turku ship yard, which has so far witnessed an investment of around €75m.
The investments were made in the machinery and information technology (IT) systems of the yard.
Meyer added: “This is a very interesting time for the shipyard’s specialists, as we are recreating the way we work and advancing our product technology.
“I’m very proud of the level of competence of our Finnish team and we are further strengthening our team with more skilled personnel from many different fields of expertise.”
As part its modernisation plan, the company is planning to increase the number of its employees from around 1,300 in 2014 to 1800 in the future.