The declaration also says no court can dissolve the Constituent Assembly, which is drawing up a new constitution. The Constituent Assembly's timeline for drafting the new constitution has been extended by two months.
President Morsi also sacked the chief prosecutor and ordered the re-trial of people accused of attacking protesters when ex-President Mubarak held office.
According to the declaration, all investigations into the killing of protesters or the use of violence against them will be re-conducted.
Trials of those accused will be re-held.
All constitutional declarations, laws and decrees made since Morsi assumed power on 30 June 2012 cannot be appealed or cancelled by any individual, or political or governmental body.
The president is authorised to take any measures he sees fit in order to preserve the revolution, to preserve national unity or to safeguard national security.
The essence of the declaration guards decisions of Morsi against annulment by the judiciary and gives him almost autocratic rule.
Egyptian opposition leader Mohammed ElBaradei accused Morsi of acting like a "new pharaoh".
ElBaradei said the new declaration effectively placed the president above the law.
"Morsi today usurped all state powers and appointed himself Egypt's new pharaoh. A major blow to the revolution that could have dire consequences," the Nobel Peace Prize winner wrote on his Twitter account.