The Ministry of Justice also revealed today that it has started feasibility work on a second large prison to be constructed in the South East of England.
The feasibility study for the proposed second big new prison is focusing on the possibility of replacing the existing Feltham Young Offenders Institution with a large new adult prison and a new youth facility on adjoining sites in West London.
The plan forms part of a major programme to overhaul the prison estate. This will see four older prisons close and the role of three others changed.
Some of the capacity will also be provided by four mini-prisons, to be known as houseblocks, at HMPs Parc, Peterborough, the Mount and Thameside, first earmarked last June
Justice Secretary Chris Grayling said: “This is the latest part of our plan to modernise our prisons, bring down costs, but to make sure that by the next election we still have access to more prison places than we inherited in 2010.
“The Feltham site in West London is a very large one, and is an obvious option for a major new project to help meet the challenges we face in London and the South East.
“I’m also really pleased that we have reached agreement on the new prison in Wrexham. It will provide a real boost to the local economy in North Wales over the next few years, which is one key reason why the Chancellor has made sure we have the money for the project.
With Treasury funding in place, work could start at the ex-Firestone factory site by next summer, pending approval.
The other changes will see HMPs Blundeston, Dorchester, Northallerton and Reading close.
HMP The Verne will be converted into an immigration removal centre, providing around 600 additional places to hold immigration detainees.
HMP Downview will change function to hold male rather than female offenders and HMYOI Warren Hill will stop holding young offenders and will also change to hold adult male prisoners.