It means there will be no option at all for inmates to purchase cigarettes.
Of those taking part in the quitting programme, almost half have managed to give up smoking already.
Prisoners who do not want to stop smoking will be able to buy e-cigarettes, and can be supported by the Help 2 Quit team should they change their minds.
New prisoners entering La Moye from January will also have access to the Help 2 Quit service's weekly clinic.
Some campaigners however have criticised the ban and instead are calling for designated smoking areas.
