Zayid, who led this OPEC member country since its foundation in 1971, died on Tuesday in his mid-80s after a long illness.
He will be buried on Wednesday in a low-key funeral confined only to family and government delegations, officials said.
Saudi de facto ruler Crown Prince Abd Allah and other Arab leaders and foreign envoys are due to arrive for the ceremony.
United Arab Emirates (UAE) newspapers dedicated their pages to paying tribute to the man who ruled "with vision" for 33 years.
"Farewell our father, our shaikh and sage of the Arab world," said al-Khaleej newspaper in its banner headline.
Saudi Arabia's Arab News daily said Shaikh Zayid was "an ideal prince".
"It would be no exaggeration to include Shaikh Zayid among the greatest Arab leaders in the 20th century."
Grief engulfed the UAE where life came to a standstill with businesses closed.
Shaikh Zayid, who received a kidney transplant in 2000, used oil income to transform seven areas into modern cities with strong economies.
Shaikh Zayid ruled the emirates
for 33 years
The country of 4.04 million people has one of the world's highest per capita incomes and expatriates make up more than 85% of the population.
Shaikh Zayid's death caused grief among his people who held him in high esteem, and in the Arab world where his traditional generosity, moderation and diplomacy won him a prominent place.
US Secretary of State Colin Powell said in a condolence statement run by the UAE state news agency: "Shaikh Zayid was a model of generosity, wisdom and leadership. The whole world knew him as a man of development, justice and civilisation."
UAE officials expected a smooth transfer of power.
Shaikh Zayid's eldest son, Shaikh Khalifa bin Zayid bin Sultan Al Nahyan, automatically took over as ruler of the capital Abu Dhabi.
Under the constitution, Vice-President and Prime Minister Shaikh Maktum bin Rashid Al Maktum, ruler of Dubai, will act as president until the federal council, which groups rulers of the seven emirates, meets within 30 days to elect a president.
Officials expect the council to elect Shaikh Khalifa president with power remaining in Abu Dhabi where 93% of the oil wealth is concentrated.
Attempt to avert war
Born in 1948, Shaikh Khalifa plays a big role in running the UAE.
He heads Abu Dhabi's Supreme Petroleum Council, which drafts oil policy, and is deputy supreme commander of the armed forces.
Shaikh Khalifa bin Zayid
Al Nahyan has taken power
The pro-Western moderniser also heads the emirate's economic body.
Statements of mourning poured in from across the world for Shaikh Zayid, famous for his 2003 initiative to avert the US war on Iraq by calling on Saddam Hussein to step down.
The sorrow was shared by millions of Arab and Asian workers who form the bulk of the country's workforce.