Brazilian construction firm Odebrecht SA and affiliated petrochemical company Braskem SA have pleaded guilty in a US court to violating American foreign bribery laws as part of a more than $3bn deal resolving a sweeping corruption probe of Brazil’s state oil company.

The companies entered their pleas in federal court in Brooklyn in the major corruption case stemming from a wide-ranging probe into their role in a scheme involving political kickbacks at Brazil’s Petrobras.

The cumulative penalties were negotiated as part of a global settlement with US, Brazilian and Swiss authorities.

They are the first guilty pleas in the United States following an investigation in Brazil dubbed “Operation Car Wash” into corruption at Petrobras, which has led to dozens of arrests and political upheaval in Brazil.

The deal with Odebrecht, Latin America’s biggest engineering firm, is for 6.9bn reais, more than $2bn, a source told Reuters this week, and is part of an agreement with Brazilian prosecutors.

Under the global settlement deal, Braskem jointly owned by Odebrecht and Petrobras, has agreed to a global deal of $632m, assistant US attorney Alixandra Smith said in court. Of that sum, the US gets 15%, Switzerland gets 15% and Brazil gets 70%, prosecutors said.

Both companies agreed to cooperate with authorities, implement compliance improvements and become subject to oversight by an external monitor.

It is one of the largest corruption cases on record. The total fines and penalties paid out by the companies exceed a 2008 agreement in which German engineering company Siemens paid $1.6bn to US and European authorities for paying bribes to win government contracts.