In a national address Saturday evening, Morsi called it a "historic day," Ahram Online reported.
"We hope to ascend into a new era of Egypt's history, to a bright future for our beloved people," he said.
"This is a breakthrough, the first truly representative constitution that protects the rights, freedoms and human dignity of all Egyptians," Ahram Online quoted Morsi as saying. "It was born out of the 25 January revolution; the last one came 175 years ago, from Mohamed Ali Pasha.
"While we stand here, we cannot forget the sacrifices of the martyrs of the revolution, and all those who were injured and their families.
"All Egyptians are adamant to see this process move forward, in order to see the objectives of the blessed revolution realized.
"All Egyptians will vote on the constitution; I hope it will be a new day for a stable and independent Egypt.'
Morsi said the referendum "will be a new step in Egypt's democratic process."
"The world looks at us and our experience with great enthusiasm; they are eager to see how Egypt will build itself," he said.
Anti-Morsi protesters gained international headlines when he announced Nov. 22 he was assuming absolute power until a new constitution was approved by parliament.
Countering days of protests by pro-democracy demonstrators, tens of thousands of Islamist supporters rallied in Cairo and Alexandria Saturday to cheer Morsi, the Middle East News Agency reported.
The Morsi supporters avoided Cairo's central Tahrir Square, the hub of anti-government protests and there were no reports of clashes or arrests.
The draft constitution passed by the Egyptian Parliament Friday is opposed by the country's top judges, the BBC said.
But Morsi, a member of the Muslim Brotherhood that espouses Sharia (Islamic law) and shuns Western values, expressed respect for the judiciary.
"I commend Egypt's judges who we highly respected, particularly for their role in overseeing the elections under the former regime and deeming them fraudulent," he said. "This great body will continue to ensure the protection of Egyptians' rights and freedoms."
At the Cairo rally, Mahmoud Saleh, 58, told Ahram Online pro-Morsi supporters were sincere.
"No one here is smoking hash -- no one here is being paid like those in Tahrir Square," he said.
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