Official results show that 77 percent of voters in Saturday’s referendum backed the changes.
Under former president Hosni Mubarak, elections were stage-managed affairs with pre-determined results and turnout was very low.
A parliamentary vote may now take place as early as September.
Mohammed Ahmed Attiyah, the head of the supreme judicial committee who supervised the vote, said 18.5 million people who voted supported the changes. Turnout was 41.2 percent of the 45 million eligible voters.
The changes include:
• Reducing presidential terms from six years to four years and limiting the president to two terms
• Obliging the president to choose a deputy within 30 days of election
• Installing new criteria for presidential candidates, including a rule that they must be over 40 years old and not married to a non-Egyptian
The country’s two main political groups, National Democratic Party and the Muslim Brotherhood, backed the proposals.
A spokesman for the Brotherhood, Essam al-Aryan, called the result a “victory for the Egyptian people”, which would allow the country to “turn a page and enter a new phase”.