The launch of European satellites on board the Russian rocket, at 00:19 GMT, was initially scheduled for December 2, but was postponed three times.
Roscosmos added via its Twitter account that the Frigat accelerator with satellites separated from the third stage of the rocket in the suborbital path. The mission will take 3 hours and 51 minutes.
The Galileo navigation system is a joint project of the European Commission and the European Space Agency.
Of the 24 Galileo satellites put into orbit, 14 were launched aboard the Soyuz between 2011 and 2016.
Four Russian missiles are scheduled to be launched from the Kourou base next year.