Mills, who ran three times for president before being elected in the closest vote in Ghana's history on a platform vowing to reform the west African country, died this afternoon at the 37th Military Hospital in Accra.
He was poised to seek re-election this year. As yet, there are no details about the cause of his death.
Mr Cameron paid tribute to the politician, describing him as a "tireless defender of democracy".
He said: "I was deeply saddened to hear about the death of President Mills earlier.
"President Mills was a tireless defender of democracy in west Africa and across the continent, and he will be greatly missed.
"Our thoughts and prayers are with his wife and family, and all the Ghanaian people on this difficult day."