The 'Candy' singer reportedly snapped up the late film director's grade II listed Woodland House in Holland Park, west London, in order to give his daughter Theodora 'Teddy' Rose a quintessentially English home.
The 39-year-old star and his wife Ayda Field have been searching for a London pad for over a year while living in Los Angeles. The plush abode is fitted with a cinema room, swimming pool, and its own editing suite.
According to The Sunday Times newspaper, flamboyant filmmaker Michael - who died at the house earlier this year aged 77 - once complained there were more than 3,400 electric bulbs in the spacious property.
Andrew Langton, chairman of Aylesford estate agents, told the paper: ''The most important thing is that Woodland House has gone to a family and not a developer, which is really what Winner wanted. That was an absolute priority so everyone is happy. I'm sure Michael will be looking down with a smile.''
The expensive sale is somewhat surprising since Robbie recently complained about the ''astronomical'' house prices in London in comparison to Wiltshire, where he already owns an £8 million seven-bedroom mansion.
He said: ''We are buying in London, so Teddy will definitely have a European accent of some sort. It's going to be Holland Park or Chelsea. But prices are astronomical. I don't know how anyone can afford to live in London full stop.
''It's gone oligarch kind of cash. It's all unrealistic. I just want to park outside the house but you can't get anywhere. It's frightening. Even garages are going for £500,000. Parking spaces are £250,000.''