SÃO PAULO—Brazilian businessman Eike Batista was jailed in Rio de Janeiro Monday after turning himself in to police over corruption allegations, marking a rapid fall from grace for the country’s once richest man.

Federal police arrested the former tycoon as he stepped off an American Airlines flight from New York, where Mr. Batista had been since authorities issued an arrest warrant on Thursday and turned to Interpol for help with the manhunt.

The entrepreneur, once a poster boy of Brazilian capitalism known for flashy antics like parking his sports cars in his mansion’s living room, was taken to Rio’s grim Bangu jail while authorities probe his alleged links to Brazil’s vast corruption scandal.

Police accuse the 60-year-old former billionaire of paying $16.5 million in bribes to the former governor of Rio de Janeiro state, Sérgio Cabral, as part of the country’s landmark investigation into bid-rigging at state-controlled oil company Petróleo Brasileiro SA, or Petrobras.

“I am fulfilling my duty as a Brazilian and returning,” Mr. Batista said in a televised interview with Brazil’s Globo shortly before boarding his flight back to Rio at New York’s John F. Kennedy International Airport on Sunday night. He declined to comment on the allegations, praising the work of Brazil’s corruption-fighting authorities. “The prosecutors are cleaning up Brazil in a fantastic way—a different Brazil is being born,” he said.