“The president can issue any decision or measure to protect the revolution,” Presidential Spokesman Yasser Ali said while reading out the constitutional declaration on television on Thursday.
“The constitutional declarations, decisions and laws issued by the president are final and not subject to appeal,” he added.
According to Ali, Morsi has also sacked Prosecutor General Abdel Meguid Mahmud and appointed Talaat Ibrahim Abdallah to replace him.
“The public prosecutor general will occupy his post for a period of four years,” the spokesman said.
Morsi tried to oust Mahmud in October following furious protests over the acquittal of a number of senior ex-regime officials.
The men were charged with involvement in the violent crackdown of popular protests in the run-up to the 2011 revolution that toppled long-time dictator Hosni Mubarak.
The new presidential decree suggests that Mubarak, who was sentenced to life in prison in June for failing to prevent the killing of revolutionaries, could face a retrial.