Quoile House cost £12m to build and is home to up to 160 inmates. It is the first accommodation block to be built at the prison in five years and it makes use of modern facilities, including a computerised system that means there are no keys.
The Prison Service say it is an open plan system that emphasises rehabilitation. There are special provisions for those with mental health concerns which mean they find it hard to cope within the general prison population.
Justice Minister David Ford described Quoile House as a "demonstration in the practicalities of prison reform".
"What we've shown is that, where we provide prisoners with better facilities, where we use those facilities for better rehabilitation, then we do reduce reoffending and we do make society safer," he explained.
The new block has four landings for those who have jobs within the prison gym or kitchen, and some inmates may meet the criteria for a low level supervision area that encourages them to spend more time out of their cell.
Offender management and safer custody are key elements in the delivery of a modern prison service.
Justice Minister David Ford
Elsewhere, the Prison Service has teamed up with Barnardo's to teach prisoners how to be better parents and develop strong bonds with their families.
David Ford added: "The provision of key workers and advisory services to engage with and assist the prisoners is a key feature of Quoile House.
"Encouraging prisoners to develop strong bonds with their families is crucial in reducing their risk of re-offending and, therefore, I am particularly encouraged by the joint venture between the Prison Service and Barnardo's in teaching parenting skills - which is a particular feature of the Quoile 3 landing."
It is hoped that further accommodation blocks similar to Quoile House will be built, but Mr Ford acknowledged that means his department will need more money.
"The current provision for capital spending is not adequate for all that we would seek to do. That's an issue we will have to look for but this is a key element of the Programme for Government for the entire Executive," he said.
But Paul Givan, chairman of the Justice Committee, said he believes the public will need to see a drop in the number of offenders committing further crimes before they will accept more money being spent on prisons.
"I think the public are going to find it difficult to justify how £12m can be spent on this facility when new schools need to be built and when hospitals are under financial pressure," he said.
"They're going to wonder where is the priority when it comes to spending tax payers' money."