The declaration also says no court can dissolve the constituent assembly, which is drawing up a new constitution.
President Mursi also sacked the chief prosecutor and ordered the re-trial of people accused of attacking protesters when ex-President Mubarak held office.
Egyptian opposition leader Mohammed ElBaradei accused Mr Mursi of acting like a “new pharaoh”.
Mr 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.
Earlier this year, Mr ElBaradei had called Egypt‘s political process “the stupidest transition in history”.
Following the new declaration, Talaat Ibrahim will replace Abdel Maguid Mahmoud as new chief prosecutor.
Mr Mahmoud’s acquittal of officers allegedly involved in attacks on protesters led to violent clashes in Tahrir Square in Cairo in October, when supporters and opponents of President Mursi clashed.
The president tried to remove Mr Mahmoud from his post by appointing him envoy to the Vatican, without giving an official reason for the switch.
But Mr Mahmoud defied the Egyptian leader and returned to work, escorted by judges and lawyers. His refusal to comply was seen as a big defeat for Mr Mursi’s push to steadily consolidate power.
The new prosecutor is now tasked with re-conducting all the investigations led by Mr Mahmoud into the alleged attacks on protesters, and re-try people already acquitted in the case.
The declaration also gives the 100-member constituent assembly two additional months to draft a new constitution, to replace the one suspended after President Mubarak was overthrown.
The re-write of the constitution, which was meant to be finished by December, has been plagued by dozens of lawsuits questioning the make-up of the constituent assembly.