Short version, Don King signed on Ali and Foreman with the promise of a $5 million purse, but didn't have the cash, so he accepted an offer to host and finance by Mobutu Sese Seko. (Wikipedia)
Don King arranged this fight with the music businessman Jerry Masucci, who took his famed musicians, Fania All Stars, to play at the venue. King managed to get Ali and Foreman to sign separate contracts saying they would fight for him if he could get a $5 million purse each. However, as King did not have the money, he began seeking an outside country to sponsor the event. Zaire's dictator Mobutu Sese Seko, eager for the publicity such a high-profile event would bring, asked for the fight to be held in his country.
There were also race relations reasons. Zaire was an independent African nation ruled by a black man, and Foreman and Ali were example of strong Black men, particularly Ali with his ties to Black Nationalism, and Mobuto was facing disapproval of his U.S. government-backed overthrow of Lumumba, so he was looking for any good publicity he could find. (Daily Beast)