All 54 countries at the organisation's congress in Cairo agreed to change the statutes which previously stopped officials serving past the age of 70.
It was proposed Caf should bring its rules in line with those of world football's governing body Fifa.
Hayatou, 68, will now be able to stand for another term in office in 2017.
His current mandate ends in two years and he is seeking four more years until at least 2021, when he turns 75.
The rule change follows success in recent years in adapting the statutes to limit potential opponents to Hayatou's rule.
Caf previously brought in a rule that candidates for its presidency can only come from the ranks of its own executive committee, a tight-knit club closely controlled by Hayatou. Fifa does not have the same restriction.
Cameroon-born Hayatou, a former athletics official, is the longest serving senior member in Fifa structures, where he acts as vice-president, and has had few serious challengers for power in Africa since first winning election in 1988.
The Confederation of African Football voted on Tuesday to remove an age limit on its officials, paving the way for Issa Hayatou to stay on as president.