His statements are the first he has made to investigators since taking refuge in Ecuador's embassy in London over four years ago to avoid extradition to Sweden for questioning in the matter.
He has said he fears Sweden would then hand him over to the United States to answer for the leaking of diplomatic cables and other classified documents by his whistleblowing website.
"I want people to know the truth about how abusive this process has been," the 45-year-old Australian said in a statement he released with the testimony.
But they are still investigating a 2010 rape allegation, which carries a 10-year statute of limitations.
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An Ecuadoran prosecutor grilled him last month over the rape claim with questions supplied by Swedish prosecutors.
Assange told the prosecutor he met the woman who has accused him of rape at a 2010 talk in Stockholm, where he was based after WikiLeaks released 75,000 secret Pentagon documents about the war in Afghanistan.
The woman, known as SW in the documents, "appeared to be sympathetic to my plight and also appeared to be romantically interested in me", adding that she invited him back to her home.
In a copy of her testimony seen by AFP, she said she woke up the next morning to find Assange having unprotected sex with her and decided to file a complaint after talking with friends.
Elisabeth Fritz, the lawyer for Assange's alleged victim, said last month it was "time for this to go to trial" after six years of legal battles.
"We are expecting that the prosecutor will announce charges after this questioning and that these charges lead to a trial in a Swedish court," she said.
But it recently returned to prominence with the leak of tens of thousands of emails from the US Democratic Party and Hillary Clinton's campaign in the final weeks of the race for the White House.
Assange denied influencing the shock election result and rejected claims he had links with Russia.
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