There has been no limit previously with incumbent Issa Hayatou leading the African body since 1988.
The 70-year-old Cameroonian has not indicated whether he will stand for re-election, but would be expected to retain his position should he do so.
In charge for 28 years, Hayatou is the longest serving CAF boss. Deceased Ethiopian Yidnekatchew Tessema was president for 16 years from 1972.
CAF spokesman Junior Binyam told AFP the change, announced during an extraordinary general assembly in Cairo, brought the African organisation in line with world governing body FIFA.
The three-term ceiling will also apply to CAF executive committee members.
Assembly delegates voted 32-16 against a Djibouti motion that CAF presidency candidates should not be restricted to executive committee members.
CAF second vice-president Almamy Kabele Camara of Guinea and executive committee member Kwesi Nyantakyi of Ghana were voted on to the FIFA Council (formerly executive committee).
Camara received 37 votes and Nyantakyi 31 to fill two vacancies with executive committee member Ahmad, a single-name Malagasy, getting 30.
Other Africans on the FIFA Council are Hayatou, Egyptian Hani Abo Rida, Constant Omari from the Democratic Republic of Congo, Tunisian Tarek Bouchamaoui and Burundian Lydia Nsekera.