Egypt beat South Africa, the only other nation to bid, by 16 votes to one with one abstention at a CAF executive committee vote in Senegal.
Original host nation Cameroon was stripped of staging duties in November because of slow preparations.
Egypt, has just six months to prepare for the expanded 24-team finals, which kick off in June. It will be the fifth time Egypt has hosted the tournament, the most recent was in 2006.
