Overall project spend of £212m is set come in substantially under the original £250m estimate, said prisons minister Jeremy Wright.
It will be the first prison in north Wales and will have capacity for 2,100 inmates.
Work has already started on the 110-acre site – which was previously the Firestone Tyre factory – and the prison will be fully operational by late 2017.
The Ministry of Justice has been particularly keen to get small and medium enterprises (SMEs) and regional companies on board during the tendering process, with a special local supplier event to help companies show the potential contractors the services they can offer.
Approximately £50m will be subcontracted to SMEs and £30m to local businesses. Half of the workforce will be recruited from the local area, including approximately 100 apprentices.