Mr Mursi, the Muslim Brotherhood’s candidate, took the oath before the Supreme Constitutional Court.
BBC reports that he promised to respect the constitution and the rule of law, and to protect the people of Egypt.
He spoke at Cairo University before going to an army base for the handover from military rule.
In the ceremony before the court, Mr Mursi said the Egyptian people had “laid the foundations for a new life, for full freedom, a genuine democracy, for putting the meaning and significance of the constitution and stability above everything else”.
He said his government would be based on the democratic pillars of “the constitutional court, the Egyptian judiciary, and the executive and legislative powers”.
There was no mention of the ruling Supreme Council of the Armed Forces (Scaf), which has dissolved parliament and issued sweeping decrees in what many Egyptians have decried as equivalent to a coup.
Mr Mursi’s administration may now try to ease the military out, knowing that in overt confrontation, the military is the one with the guns, says regional analyst Magdi Abdelhadi.