Low Moss jail was praised for its attempts to create links with the local community and with voluntary groups, and for its treatment of prisoners.
The inspectors singled out activity nights involving local scout and cub groups which prisoners' children attend.
The jail was opened in March last year to house around 700 prisoners some on remand, but most serving terms of less than four years.
The report by Her Majesty's chief Inspector of Prisons David Strang said the jail's inmates are treated with decency, humanity and their legal rights are respected.
It noted there were weekly education classes, yoga for the over 50s and unlimited visits.
The inspection said the dedicated children's visits to improve parenting, was a model for the rest of Scotland.
The report noted:
l Support service for prisoners with addiction or mental health issues.
l Food is adequate for health, with adequate portions, but occasionally food may deteriorate to a degree during transportation.
l Cells had adequate natural light and ventilation with access to drinking water and toilet and showering facilities.
l Relationships between prisoners and staff are good.
l The library is neither well used nor well stocked.
l Pharmacy services are available but arrangements are inconsistent.
Mr Strang said: "Overall, this is a good and positive report on HMP Low Moss. I am particularly impressed with the links that have been fostered with local groups and the community.
"Access to purposeful activity and visits also deserve to be singled out for praise.
"A clear positive culture and can-do attitude has been created and bought into by both staff and managers.
"This has all been achieved in a relatively short time and is testimony to the vision and ethos of the management team and staff."
The inspection took place between May 13 and May 21 this year at the Bishopbriggs jail.
Mr Strang issued a number of recommendations including ensuring there is adequate first aid cover at all times. He also said prisoners should be provided with sufficient, appropriate storage facilities in the cells.