The 53-year-old Bradley agreed to a deal worth $37,000 a month until after the 2014 World Cup in Brazil.
“I’m proud to take over as coach of Egypt,” Bradley said at a news conference.
“I’m looking forward to dealing with the players.”
Bradley’s first match in charge is an exhibition against five-time world champion Brazil in November.
Longtime coach Hassan Shehata stepped down in June after Egypt collected two points from four African Cup qualifiers.
A subsequent loss to Sierra Leone confirmed Egypt’s failure to qualify for a tournament it has won on the past three occasions.
The record seven-time winners will not compete in the continental championship for the first time in 33 years.
Bradley was fired as U.S. coach in July after more than four years in charge and replaced by Jurgen Klinsmann.
His main task will be to try to qualify Egypt for the World Cup for the first time since 1990. Egypt is favored to emerge from a group which also includes Guinea, Zimbabwe, Comoros and Mozambique.
Bradley’s assistant hasn’t been hired, but the Egyptian Football Association said it would be a local coach.
Bradley led the U.S. to the final 16 of the World Cup last year and signed a contract extension until 2014 as a result.
But even as Bradley was given a new deal, there were concerns the team had stagnated under his leadership.
A Gold Cup loss at home to Mexico in June was critical in his departure.