Cusick died of heart failure in his sleep on Thursday, the BBC reported.
The Daleks are the villains on the cult science fiction series "Doctor Who," which will be celebrating its 50th anniversary this year with a number of events.
The official 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."
Doctor Who actor and writer 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!"