The school provides all levels of education from kindergarten to high school and was established under the name so-called Rainbow Association.
Demirli added that the school would facilitate the peoples of Turkey and Ethiopia getting to know each other better.
He expressed pleasure at having taken over the school after efforts lasting two years.
Demirli said the group was working on taking over other FETO-linked schools across Ethiopia.
FETÖ and its U.S.-based leader Fetullah Gülen orchestrated the coup which left 251 people martyred and nearly 2,200 injured.
Turkey also accuses FETÖ of being behind a long-running campaign to overthrow the state through the infiltration of Turkish institutions, particularly the military, police, and judiciary.
FETÖ has a considerable presence abroad, including private schools which serve as a revenue stream for the terror group.
Hurriyet Daily News