The news of his demise was confirmed on Sunday morning on his Twitter page, reports telegraph.co.uk.
"We are very sad to say that Ginger has passed away peacefully in hospital this morning. Thank you to everyone for your kind words over the past weeks," a statement read.
The musician whose real name was Peter Edward Baker suffered from osteoarthritis, chronic obstructive pulmonary disease and a long battle with drug addiction, and underwent heart surgery three years ago.
The exact cause of his death is not known yet.
The band, which released four albums and sold more than 15 million records, propelled guitarist Eric Clapton to international superstardom and solidified Baker's reputation as one of the UK's greatest ever drummers.
Despite Cream's split after just two years, Baker and Clapton re-emerged in 1969 as part of the blues rock band Blind Faith, alongside Steve Winwood and Ric Grech.
Baker's last album was "Why?", which released in 2014 .