Aliyev, 80, had been hospitalised in Cleveland since 6 August where he was being treated for heart and kidney problems.
He was flown to Turkey and then America for treatment after collapsing while giving a speech live on television in January.
Aliyev was one of the top officials in the former Soviet Union who kept a grip on power after the collapse of communism.
A former general in the Soviet intelligence, the KGB, he was named the communist party's first secretary in Azerbaijan, and became a member of the Soviet Communist Party politburo.
He was elected president of the independent Azerbaijan in 1993.
Aliyev was widely criticised abroad for corruption in his country and for his authoritarian rule. But many Azeris still respected their leader, who they called "Baba", or grandfather.
The former president's son, Ilham, won widely discredited elections in October to take over the presidency from his father.
Tahir Taghi-Zadeh, a spokesman for the Azerbaijan embassy in Washington, said the former president's body would be flown back to Azerbaijan in the next two days.