The red brick terrace at 9 Newcastle Road, Wavertree, was where the member of The Beatles lived from birth, in 1940, until he was five.
Auctioneers said a telephone bidder, who wanted to remain anonymous, was the successful buyer after a "bidding war".
The three-bedroom house had been given a guide price of between £150,000 and £250,000.
The property has a rear yard and is a few streets away from Penny Lane, made famous by The Beatles.
Andrew Brown, from Countrywide Property Auctions, said: "There was a lot of interest in the property before the auction from potential buyers who lived in the UK and internationally."
John Lennon's first home, in Liverpool, has been sold for £480,000 at an auction held at the Cavern Club.