The German line, owned by hotelier Seaside Collection, now owns five vessels which previously belonged to Crystal having already purchased Mozart last autumn.
From April, Riverside will offer Danube sailings onboard Mozart, while Ravel will operate itineraries along the Rhone and Saone and Debussy will cruise the Rhine.
Bach and Mahler are slated to return to operations for 2024 and itineraries will be announced later this year.
The news comes as the latest stage of expansion by Riverside, having hired former AmaWaterways UK boss Stuart Perl as its managing director.
"We are thrilled by the expansion of our fleet to include these storied vessels," said Seaside Collection owner and Riverside founder Gregor Gerlach. "This acquisition allows us to expand our itinerary offerings, showcasing a level of space, personalised service and elegance not found with any other river cruise line."
The line said it wanted to be "defined not only by its crew-to-guest ratio but by its service culture", which it described as "authentically personal" with butlers offering 24-hour room services and "one-of-a-kind" excursion experiences.
