It adjoins the eight-bedroom property the couple live in with children Lourdes, 10, and Rocco, six.
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They also own two nearby mews houses, which are occupied by staff, and two other houses in central London.
Madonna, 48, and British film director Ritchie, 38, bought their latest home from designer-developer Paul Davies, who made headlines recently by asking a record £40,000 a week in rent for one of his Mayfair properties.
The couple paid almost twice the £3.1million Mr Davies spent when he bought the property in August last year, even though he has not refurbished it.
The house has six floors and includes a vaulted artist's studio which adjoins the garden wall of the family's main home.
A source said: "Madonna has been a very shrewd investor in property - this is her fourth in the area. She knows the prices are significantly lower than in Mayfair but that the area is coming up. She has said she'd like to buy the whole street.
"She was really keen to get her hands on this house because she knows once Paul Davies starts developing properties an area can skyrocket in price. She was calling him for eight months and her initial offers were rejected, but after a series of meetings he agreed to sell."
Madonna faced competition for the house from comedian Jennifer Saunders and photographer Mario Testino.
Mr Davies refused to comment but he has described the property, a former private clinic, as "a blank canvas" in need of renovation.
The house has oak floorboards and many original features.
Madonna complained recently about workmen renovating her home, saying: "I can't believe how people don't like to work. The week starts at noon on Monday and ends at noon on Friday. I'm used to people in America working seven days a week."
It is not known whether the family intend to connect their acquisition to their existing home or rent it out.
Madge's property portfolio
Country home: Ashcrombe House on Madonna and Guy's Wiltshire estate
Their portfolio includes six properties in central London.
In Marylebone there is their £7 million family townhouse, the new £6million property and two mews cottages close by, one of which was bought last year for £900,000.
The singer has also bought two properties that are used by the Kabbalah religious sect. One - a £3.6 million building in the West End - is used as headquarters by the group.
The other is a £1.6 million, fivestorey Georgian townhouse in Conway Street, Regent's Park. The couple also own the 1,200-acre Ashcombe estate in Wiltshire, formerly owned by Sir Cecil Beaton, which they bought for £9 million in 2001.
In the United States they have an £8 million house in Beverly Hills and an apartment in New York.--