Those caught breaking the ban would also get three penalty points on their driving licences for each offence.
Under current laws motorists can only be prosecuted for using mobiles if they fail to keep proper control of their vehicle. The Government announced it was considering the law change last August and has carried out a public consultation on its proposals which, it said, demonstrated overwhelming support for a ban.
The planned new law will have to be approved by Parliament and be added to the Road Vehicles (Construction and Use) Regulations.
Road safety minister David Jamieson said: 'We are all too familiar with the sight of people driving along while holding and talking on their mobile phones. Any driver will be distracted by a phone call or text message. It affects the ability to concentrate and anticipate the road ahead, putting the driver and other road users at risk.
'Our decision to introduce this new offence will make the roads safer for us all. Missing a call won't kill you - an accident quite possibly could.'
In the new law the definition of driving includes using a phone while the car is stationary with the engine running. Hands-free mobile phones are not included in the law because the Government concluded, a ban would be 'difficult to enforce'.