In a 1,800-word statement, "John Doe" reveals he has never worked for a spy agency or a government.
He starts the statement by citing "income equality" as a motive.
The Panama Papers have shown how some wealthy people use offshore firms to evade tax and avoid sanctions.
The papers belonged to the Mossack Fonseca law firm. It denies any wrongdoing and says it is the victim of a hack.
The papers were investigated by hundreds of investigative journalists, including from the BBC, who worked in secret with the International Consortium of Investigative Journalists (ICIJ) for months.
The documents have revealed the hidden assets of hundreds of politicians, officials, current and former national leaders, celebrities and sports stars.
They list more than 200,000 shell companies, foundations and trusts set up in tax havens around the world.
The John Doe statement came shortly before US President Barack Obama delivered an address on the economy, in which he cited the Panama Papers as highlighting the problem of corruption and tax evasion.
He said the US would require banks to identify those behind shell corporations. Mr Obama said his administration's actions would allow it to do a better job of making sure people paid taxes.
Although the name John Doe is used, the gender of the source has not been revealed.
In the statement, The Revolution will be Digitized, John Doe starts by saying: "Income equality is one of the defining issues of our time."
He adds: "Banks, financial regulators and tax authorities have failed. Decisions have been made that have spared the wealthy while focusing instead on reining in middle- and low-income citizens."
He goes on to say: "Thousands of prosecutions could stem from the Panama Papers, if only law enforcement could access and evaluate the actual documents.
"ICIJ and its partner publications have rightly stated that they will not provide them to law enforcement agencies.
"I, however, would be willing to co-operate with law enforcement to the extent that I am able."
But he adds: "Legitimate whistleblowers who expose unquestionable wrongdoing, whether insiders or outsiders, deserve immunity from government retribution."
Responding to speculation about his or her identity, John Doe's statement says: "For the record, I do not work for any government or intelligence agency, directly or as a contractor, and I never have.
"My viewpoint is entirely my own, as was my decision to share the documents with Suddeutsche Zeitung and the International Consortium of Investigative Journalists (ICIJ), not for any specific political purpose, but simply because I understood enough about their contents to realise the scale of the injustices they described."
John Doe says that global judicial systems have "utterly failed to address the metastasizing tax havens spotting Earth's surface".
He says: "I decided to expose Mossack Fonseca because I thought its founders, employees and clients should have to answer for their roles in these crimes, only some of which have come to light thus far.
"It will take years, possibly decades, for the full extent of the firm's sordid acts to become known."
Panama-based Mossack Fonseca says it was hacked by servers based abroad and has filed a complaint with the Panamanian attorney general's office.
It says it has not acted illegally and that information was being misrepresented.
Panama Papers - tax havens of the rich and powerful exposed
* Eleven million documents held by the Panama-based law firm Mossack Fonseca have been passed to German newspaper Sueddeutsche Zeitung, which then shared them with the International Consortium of Investigative Journalists. BBC Panorama and UK newspaper The Guardian are among 107 media organisations in 76 countries which have been analysing the documents. The BBC does not know the identity of the source
* They show how the company has helped clients launder money, dodge sanctions and evade tax
* Mossack Fonseca says it has operated beyond reproach for 40 years and never been accused or charged with criminal wrongdoing
* Tricks of the trade: How assets are hidden and taxes evaded