The former United States national team coach will be in charge of the Pharaohs for the next three months, at which point a decision will be made concerning his future
The north Africans failed to reach the 2013 Africa Cup of Nations after it was shocked by Central African Republic in the qualifying preliminaries, losing 4-3 on aggregate.
Chairman of the EFA committee Anwar Saleh said that Bradley will still be at the helm of the Pharaohs for the next three months, and in September a decision on his future will be made.
"We leave the decision regarding the survival of the technical staff to the new board, which will convene in September," he told Goal.com.
The seven-time African champions remain in contention to reach the 2014 World Cup in Brazil, after a positive start to that qualifying campaign, winning both of their matches.
The Pharaohs beat Mozambique 2-0 at home before defeating Guinea 2-3 in Conakry during the month of June to top Group G of the qualifiers.
Azmi Megahed of the EFA spoke at a press conference and revealed, "We will therefore not be prejudge and will study the report he gives us on the game we lost. I personally don’t want him gone because we still have the World Cup qualifiers and he did quite well in those."