"I am confident that we will work together to accelerate Play Two's digital transition and open up new music segments to digital with our shared expertise and innovation."
The deal gives KKR a position in the business whose live division, BookMyShow Live, has staged concerts in India by Coldplay, Ed Sheeran, Travis Scott, Guns N' Roses and Post Malone.
The proceeds from the CBS deal will be donated to World Central Kitchen, which provides meals to communities affected by natural disasters and civil unrest.
The launch makes YouTube Music the latest to offer the feature as rivals Spotify, Amazon Music and Deezer have already rolled out the same tool in recent years.