"Unfortunately, at 6:20 pm local time (2150 IST) our historic leader passed away," Joseph Kasios said outside the Nicosia clinic where Clerides had been hospitalised.
Cypriot leaders paid tribute to Clerides, with President Nicos Anastasiades telling state media he was "like a father to me" and House Speaker Yannakis Omirou calling him a "true statesman."
"I am emotionally distraught. Glafcos Clerides was like a father to me," Anastasiades said from Sri Lanka, where he is attending the Commonwealth Summit.
Omirou added: "Some people write history; he (Glafcos Clerides) was the history of Cyprus, a true statesman."
The White House said the United States was "saddened" by Clerides' death.
"Throughout his life, President Clerides was devoted to the highest principles of public service, human rights, international cooperation, and peace," spokesman Jay Carney said in a statement.
Carney said Americans would never forget the sympathy and support Clerides offered after the killing of US Ambassador Rodger Davies and his Cypriot assistant Antoinette Varnava in 1974 by a Greek Cypriot sniper.
A World War II veteran, Clerides was admitted to Evangelistria clinic on Wednesday in a "very grave condition" aggravated by serious illnesses in the past few years and his advanced years, his doctor said.
An AFP reporter said flags were flying at half mast outside the ruling party headquarters after news of Clerides's death.
Clerides was seen as instrumental in guiding Cyprus towards accession to the European Union in 2004.
But despite his own support for reunification efforts, Cyprus entered the bloc a divided island after Greek Cypriots voted in a referendum the same year to reject a UN plan that would have reintegrated the breakaway Turkish Cypriot north.
