The Basque-born artist passed away in his sleep at his home in San Sebastian on Monday after a prolonged battle with pneumonia and Alzheimer's disease.
His career saw him become one of Europe's best-known artists and his trademark giant metal sculptures were erected in places as far afield as Berlin and Texas.
Spain's leaders lined up to pay tribute to the "Man of Iron", with King Juan Carlos praising the "poetry and humanity" of his work in a message of condolences.
In the sculptor's beloved San Sebastian, the flag on the city hall was lowered to half-mast to mourn his death.
"This had to come, we were all expecting it," said his son, Luis Chillida. "He did not suffer, but simply slipped into sleep and stayed that way."
"One of the great modern artists and sculptors of the 20th century has disappeared," Spain's Culture Minister, Pilar del Castillo, said.
Winner of prestigious international prizes and a member of arts academies worldwide, Chillida designed a giant monument to German reunification near the Chancellery in Berlin: two cast-iron hands weighing 88 tonnes.
In Spain, he is perhaps best remembered for his Comb of the Wind - twisted, tree-like sculptures on the coast at San Sebastian. The work featured on the now-defunct peseta coins.
Demonstrators for peace in the Basque region, where a separatist struggle with Madrid has left more than 800 people dead since 1968, have often used the monument as a focus for their rallies.
Eduardo Chillida is due to be cremated on Tuesday and his ashes interred at the Chillida Museum in the Basque town of Hernani.