The squatters managed to get gas, electricity and hot running water switched on, and set up a Wi-Fi account aptly named "billion".
Squatter Tom Fox, 23, told The Sun the group had planned to use the house as a homeless shelter, accusing Mr Goncharenko of leaving it "to rot".
"We've said jokingly if the owner gives us £50,000, we'll leave," Mr Fox said.
"I don't think I'd want to sit down and have a discussion with him - I don't know him, but I don't think we'd agree on things ... It's just making a point about fighting capitalism with capitalism."
Squatting should be legalised, he argued, saying: "Why don't they open up vacant, habitable buildings and assign volunteers to keep watch and look after homes?"
The squatters posed triumphantly on the front balcony of the property, where a black flag bore the name "Antifaschistische Aktion" - a European anti-fascist organisation.
Credit: Twitter / @LauriLoveX
Mr Goncharenko has reportedly bought four luxury London properties in the past three years, including Hanover Lodge in Regent's Park, for which he paid $196 million - making it one of Britain's most expensive homes.
The billionaire has been described as "an obscure figure even in the secretive world of Russian oligarchs", with the source of his wealth unclear and his investments made through a network of offshore holding companies.
Alleged computer hacker Lauri Love, 32, bragged of squatting at the Eaton Square property, tweeting images of its interior to his followers.
Mr Love, who faces up to 99 years in prison if extradited to the US, is accused of stealing data from US agencies including the FBI and NASA.