Saudi authorities released billionaire Mohammed Hussein Al Amoudi after nearly 15 months of detention, Ethiopian officials said, the latest in a wave of prominent businesspeople to regain their freedom after being rounded up in November 2017.

Mr. Al Amoudi, born in Ethiopia and a Saudi citizen, was once considered one of the world’s richest people, with a net worth of as much as $15 billion, according to Forbes. But his still unexplained detention raised questions about his ownership of a far-flung business empire that includes...