The announcement was made on Tuesday morning on the London Stock Exchange after current operators, Stagecoach, withdrew halfway through a contract that was due to end in 2017.
The timing caused surprise as the network, known as Metrolink, is in the middle of a £1.4 billion (€1.6 billion) expansion programme.
Trams will now be run by RATP Dev UK, a subsidiary of government-owned RATP.
The Manchester tram network was opened in 1992 and carries 20 million passengers a year on 40 kilometres of track.
"Metrolink is one of the UK's most successful tram networks, so we are naturally delighted to join with the existing team to be able to bring our expertise and know-how to continue its further development," said Paul Matthews, chief executive of RATP Dev UK.
In France, some seemed less than thrilled at the news. "Will they import our strikers as well?" asked one commenter on Le Figaro's website. Another said "RATP would do better to improve their current network rather than investing elsewhere."
RATP is one of the world's biggest transport companies with operations in 12 countries. Its UK subsidiary is already well-established with 3,000 employees and revenues of more than €220 million. The company runs buses in London, Bath and Bournemouth.