Mohammed Morsi began by moving into the office of former President Hosni Mubarak. He also started consultations on forming his team and a new government, an aide said.
Meanwhile, Egypt's benchmark stock index closed with record gain of 7.5 percent.
On Sunday, Morsi made his first televised speech to the country. In Tahrir square in Cairo, joyous supporters wept and kneeled in prayer when Morsi addressed them.
This is considered a stunning victory for the Muslim Brotherhood, a group that was outlawed under Mubarak.
Morsi is the first Islamist to become president. He also has ties to Southern California. He received his doctorate at USC and he taught at Cal State Northridge.
The Associated Press contributed to this report.