SÃO PAULO—Less than a year after Brazil’s president was impeached, her successor is at the center of explosive bribery allegations in the ever-widening corruption probe that has engulfed the country’s leadership class.

One of the country’s largest companies admitted on Friday to paying bribes to President Michel Temer and his predecessors, Dilma Rousseff and Luiz Inácio Lula da Silva, implicating all of the nation’s leaders for the past 14 years.

The revelations in documents released by the country’s Supreme Court Friday are the latest and most damning episode yet in a three-year investigation into graft at state-run oil company Petrobras that has ravaged the country’s political establishment and raised fears over the future of Latin America’s biggest economy.

Executives at Brazil’s giant meatpacker JBS told prosecutors the company paid a total of $123 million in bribes to the country’s politicians over recent years, including payments of at least $2.2 million to Mr. Temer. Joesley Batista, chairman and heir of the family-run pork-and-chicken empire, said he deposited $30 million in an offshore bank account for Ms. Rousseff, the leftist leader who was impeached last year, in exchange for loans from Brazil’s state development bank BNDES.

He also told prosecutors he deposited at least $50 million into an offshore account held by Mr. da Silva, the popular former president who is still seen as possible presidential candidate despite facing several trials for his alleged role in the corruption scheme. Mr. Batista said Ms. Rousseff and Mr. da Silva had $150 million in offshore accounts in 2014.