Morsi took the oath before the general assembly of the High Constitutional Court, comprised of 18 top judges, Ahram Online reported.
"May God assist you with the challenging task you are taking on," lead judge Farouk Sultan told Morsi before he took the oath.
Morsi was sworn in under the June 17 Constitutional Declaration, which the Muslim Brotherhood and secular revolutionary groups have protested against. The declaration gives the military authority and limits the powers of the new president.
Ahram Online said Morsi was to have been sworn in before Parliament, which was effectively dissolved by a June 14 Constitutional Court ruling. Protesters have demanded reinstatement of Parliament.
The Supreme Council of the Armed Forces, Egypt's ruling military council, specified in an addendum to the Constitutional Declaration that the new president would be sworn in before the general assembly of the High Constitutional Court instead of parliament.
After Saturday's swearing-in, which was broadcast live on state television, Morsi was to deliver his inaugural speech at the main campus of Cairo University.
On Friday, Morsi took an unofficial oath in Tahrir Square.
"Free revolutionaries will continue the course," Morsi chanted with the crowd before his speech.
In the Friday speech, Morsi said: "Revolution is led by its aims, and it will continue until it achieves all of its goals. You are the source of legitimacy and power, above all."
Morsi said he would work for the release of civilians detained by the military and seek justice for those who had been killed and injured in last year's uprising.
The BBC reported Morsi also said he would work to free Omar Abdel-Rahman, an Egyptian-born Islamist convicted after the 1993 World Trade Center attack of plotting to bomb several New York City landmarks.