The largest female prison in western Europe, Holloway in north London is being closed as part of government plans to sell off city-based prisons to turn into housing and build more modern facilities further away.
"Old Victorian prisons in our cities that are not suitable for rehabilitating prisoners will be sold," Osborne told parliament.
"I can tell the House that Holloway prison -- the biggest women's jail in western Europe -- will close," he said.
The Victorian complex was torn down and completely rebuilt between 1971 and 1985.
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Well-known inmates have included "Moors murderer" Myra Hindley and serial killer Rose West.
Before it was redeveloped, it also housed many leading suffragettes detained for taking part in militant protests as women pushed for the vote in the early 1900s.
Some were force fed in the prison after going on hunger strike, making it a symbol of women's rights.
Five women were executed at the prison, Ruth Ellis being the last in 1955. The outrage provoked by her hanging helped sway public opinion, and eventually the law, against capital punishment in Britain.
The government has set aside 1.3 billion pounds (USD 1.9 billion, 1.8 billion euros) for the overhaul of the prison system.