A former executive named Liss-Olof Nenzell has handed the US Securities and Exchange Commission (SEC) documents relating to the alleged kickbacks, Dagens Nyheter daily and Swedish public radio SR said.
"Enormous sums were sent via Zurich from the company headquarters in Sweden to secret recipients around the world," Dagens Nyheter said, referring to what it called Nenzell's central role in the scheme.
The newspaper said the biggest bribes included 1.4 billion kronor (140 million euros, $150 million), sent to bank accounts in Malaysia, and 763 million kronor sent to Poland, via the British offshore banking haven of Jersey.
SR, meanwhile, said money was sent to politicians and senior civil servants to Costa Rica, including the then president, Miguel Angel Rodriguez, "at a time when Ericsson was vying for a major state contract in telecoms."
SR also said it had testimony from "several former top executives," who speaking on condition of anonymity "recounted how they were guilty of active corruption in securing contracts in a large number of countries."
Allegations of systematised bribery in Ericsson date back to 2010 in the Swedish media, but the company has always denied any wrongdoing.
Quoted by Dagens Nyheter, it said Wednesday it never found "any evidence that bribes were allegedly paid."
In June, Ericsson said it was being investigated, including in the US, over what the Swedish press said was a case of alleged corruption in China, and in Greece.