His daughter, Claire Heawood, said that he died of heart failure in his sleep on Thursday.
The Doctor Who Magazine tweeted: "It's with great sadness that we report the death of Ray Cusick - the designer of the Daleks. Half a century on, his iconic design lives on."
Mark Gatiss tweeted: "Farewell to the great Ray Cusick. His passing is especially sad in this anniversary year but his creation remains immortal. Daleks forever!"
He leaves behind two daughters and seven grandchildren.
R.I.P. Ray Cusick.