'My mother, the grandmother to my beautiful little girl, passed away late last night,' wrote Seymour Platt on Facebook.
'She suffered in the last few years with Chronic Obstructive Pulmonary Disease but lost the fight.'
Keeler was alleged to be sleeping with British Secretary of State for War John Profumo while conducting an affair with a Russian defence attache during the height of the Cold War , rocking Harold Macmillan's Conservative administration in 1963.
'She earned her place in British history but at a huge personal price,' wrote her son. 'We are all very proud of who she was.'
Profumo, who later resigned in disgrace, was said to have been introduced to showgirl Keeler through osteopath Stephen Ward at a party.
The scandal likely contributed to Macmillan's election defeat to Labour's Harold Wilson in 1964.
The then-model Keeler, aged 19 at the time, gave newspaper interviews during the crisis, and posed naked on a chair in an iconic photograph.
The affair was immortalised on film with 1989's 'Scandal', in which British actress Joanne Whalley played the role of Keeler.
The mother-of-two had recently been living under the name Sloane.