A midfielder in his playing days, Gharib, was a member of the Egypt side that won the 1986 Nations Cup.
The 54-year-old's first assignment will be to guide Egypt to the 2015 Nations Cup finals in Morocco after they surprisingly failed to reach the last two tournaments.
Bradley took Egypt to the last round of African qualifying for next year's finals but his contract was not renewed after The Pharaohs were thrashed 7-3 on aggregate by Ghana over two legs earlier this month.
(Reporting by Mark Gleeson in Cape Town; Editing by John O'Brien)
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