Former auto titan Carlos Ghosn, packed into a case typically used for concert audio equipment, was sneaked onto a private jet at an airport in Osaka, Japan, late Sunday, according to people familiar with the matter, in what has become one of the corporate world’s most stunning cases of bail jumping.

His escape from Japan, where he was fighting charges of financial crime stemming from his time at the top of Nissan Motor Co. and Renault SA, was months in the making, according to people familiar with the matter, and was put in...