Number 10 Admiral Grove, Toxteth, was sold following the death of "well-respected" tenant Margaret Gorse, its former owners Plus Dane Housing said.
The new owner is Beatles fan Jackie Holmes, who has previously bought properties connected with John Lennon and George Harrison.
She paid £15,000 over the guide price at the auction held at the Cavern Club.
Restrictions on the sale would mean it could not be turned into a tourist attraction or museum, a Plus Dane Housing spokeswoman said.
Starr moved into the terrace from nearby Madryn Street as a small child and lived there before finding fame.
He spent most of his formative years at the property, learning the drums and celebrating his 21st birthday party there.
The home became a regular haunt for the Fab Four as they honed their seminal sound.
Starr paid homage to the house in his 2008 song Liverpool 8, and The Empress pub at the end of Admiral Grove appeared on the front of his first solo album, Sentimental Journey.
Part of the official Beatles Tour, the property still attracts fans daily.
Plus Dane Housing said profits from the sale would be reinvested to improve other properties in the area.
Source: BBC/National Trust
Read more: Where did the Fab Four live in Liverpool?
The childhood home of Beatles drummer Ringo Starr has been sold for £70,000 at auction in Liverpool.