Question: He denies the allegation that he raped a Swedish woman in 2010.
Swedish prosecutor Ingrid Isgren listened as an Ecuadorean prosecutor put the questions to Mr Assange.
He took refuge in the embassy four years ago, fearing extradition. He says the sex was consensual and believes the allegations are politically motivated.
The accusations relate to a visit Mr Assange made to Stockholm in August 2010 to give a lecture.
Ms Isgren and Swedish police inspector Cecilia Redell left the embassy at 13:30 local time (13:30 GMT) without making any statement to the media. They may continue questioning Mr Assange for several days.
Q&A: Julian Assange and the law
Mr Assange has refused to travel to Sweden for questioning citing concerns he would be extradited to the US over Wikileaks' release of 500,000 secret military files on the Afghanistan and Iraq wars. However, lawyers argue that his extradition from Sweden would be even less likely than from the UK.
Mr Assange is accused of raping a woman, named in legal papers as SW, at her home in August 2010.
Swedish prosecutors dropped part of their investigation last year because of a statute of limitations.
Mr Assange is "not hiding" at the embassy, but he will not go to Sweden because he would thereby risk losing his Ecuadorean asylum status, his lawyer Jennifer Robinson told the BBC on Monday.
"Sweden refused to provide assurances against onward extradition to the United States," she said, accusing the Swedish authorities of "dragging their feet" over the case.
It's taken many months of tortuous diplomatic and legal exchanges just to get the Swedish prosecutor in the door.
Under the agreement worked out with Ecuador, the Swedes were not allowed to question Julian Assange directly. Instead questions were to be submitted in Spanish and put to the Wikileaks founder by an Ecuadorean prosecutor.
No follow-up questions were allowed.
This may explain why the Swedish prosecutor had been reluctant to question Julian Assange in London, insisting it would "lower the quality of the interview". She changed her mind in March 2015, a few months before lesser allegations made against Julian Assange had to be dropped because of a time limitation.
At the embassy Mr Assange is beyond the reach of the UK authorities. Sweden has issued an arrest warrant for him, which he has appealed against.
Shortly after Ms Isgren entered the embassy, a cat - said to belong to Mr Assange - appeared at one of the windows and began watching the journalists and Assange supporters gathered outside.
The cat has its own Twitter feed, which says it lives with Mr Assange and is "interested in counter-purrveillance".
A statement on behalf of the Swedish prosecutors, quoted by the Press Association, said the investigation would remain confidential.
"Therefore, the prosecutors cannot provide information concerning details of the investigation after the interview," it said.
One of Mr Assange's lawyers, Per Samuelson, said his client "is very happy that he finally will be given the opportunity to give his statement to the Swedish prosecution.
"He has been waiting for this for over six years. He has prepared himself very carefully and will give a statement and will co-operate to the full extent."

Sum: Sweden's chief prosecutor has questioned Wikileaks founder Julian Assange about a rape allegation at the Ecuadorean embassy in London.
Article: Addressing a meeting, Alexander Zakharchenko said the fighters had trained "four months on the territory of the Russian Federation".
The rebels, he said, had reserves of 150 combat vehicles, including tanks.
An earlier mistranslation of his words suggested Mr Zakharchenko had said the vehicles were on their way from Russia.
Russia has denied claims by Ukraine and Western reporters that military aid to the rebels has been crossing the border.
More than 2,000 civilians and combatants have been killed since mid-April, when Ukraine's new government sent troops to put down an uprising by pro-Russian separatists in the Donetsk and Luhansk regions.
A huge humanitarian aid convoy from Russia is stalled on the Russian side of the border about two hours drive from Luhansk, apparently awaiting inspection by Ukrainian border guards.
Red Cross official Pascal Cuttat said on Saturday there were still no security guarantees in place for his staff to escort the lorries, although "technical conditions" had been agreed with Ukraine and Russia for crossing the border.
On Friday Russian Defence Minister Sergey Shoygu assured his US counterpart Chuck Hagel that there were no Russian military personnel involved with the convoy, nor would it be used as a pretext for a Russian military intervention.
Journalists who were invited to inspect some of the 280 or so vehicles on Friday found humanitarian aid inside but also noticed that some of the lorries were not full to capacity.
Mr Zakharchenko, who became the prime minister of the self-declared Donetsk People's Republic (DPR) last week, made the announcement to the rebels' parliament on Friday, with a video of his speech (in Russian) posted on YouTube.
Littering the speech with military jargon, he said: "There are, at present, in the axis of the corridor [linking rebels in Donetsk with those in Luhansk and the Russian border] - there have been assembled -reserves of the following order: 150 units of military hardware of which about 30 are actual tanks and the rest are infantry fighting vehicles and armoured personnel carriers, and 1,200 personnel who underwent four months of military training on the territory of the Russian Federation."
The rebel leader went on a Russian pro-Kremlin TV channel on Saturday to reject reports that the hardware had come from Russia.
"The Ukrainian military have left us so much hardware that we can't find enough people to crew it - I mean tanks, troop carriers, Grad [multiple rocket] launchers and so on," he told Life News (video in Russian).
He added that "ethnic Ukrainian" volunteers from Russia, not servicemen, were fighting for the rebels, along with "Turks; a great many Serbs; Italians and Germans; and even two Romanians".
Ukraine said on Friday it had partially destroyed an armoured column that had crossed from Russia on Thursday evening. Two UK newspaper reporters witnessed the alleged incursion.
Russia's defence ministry responded by saying the incursion reports were "some kind of fantasy" and Moscow has consistently denied directly arming or training the rebels.
But the incident prompted a flurry of Western condemnation.
"Any unilateral military actions on the part of the Russian Federation in Ukraine under any pretext, including humanitarian, will be considered by the European Union as a blatant violation of international law," a statement by EU foreign ministers issued on Friday says.
German Chancellor Angela Merkel told Russian President Vladimir Putin in a phone call on Friday to "put an end to the flow of military goods, military advisers and armed personnel over the border".
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Summarize:
Answer: The new rebel leader in east Ukraine's Donetsk region has said his forces include 1,200 fighters who underwent military training in Russia.