The Prison Service will own the Wrexham jail, which will house 2,000 men.
Just 34% of it will be run by private and voluntary organisations.
The prison will be category C - for inmates who cannot be trusted in open conditions but who do not have the resources and will to make a determined escape attempt.
A new £212m super-prison will be publicly run, with a third of it outsourced to the private sector or charities.