The Â£212m category C "super-prison" HMP Berwyn can house 2,106 offenders, making it the largest in the UK.
Work began on the site on the Wrexham Industrial Estate in May 2015 and recruitment has been under way for just over a year.
The Ministry of Justice said the prison would open "at the end of February" but would not confirm an exact date.
Wrexham's new prison will accept its first inmates on 27 February, the BBC understands.