Garfield will join other high profile business leaders in the group which will meet on a quarterly basis with David Cameron to give him high level advice on industry concerns about policy and economic issues.
Her appointment comes as the prime minister overhauled the panel which acted as a sounding board for him when he was leading the coalition government.
The other new members include BP chief executive Bob Dudley, Easyjet chief executive Carolyn McCall, EY chairman Steve Varley, Asda chief executive Andy Clarke, and Rolls Royce chief executive Warren East.
The EU referendum, which Cameron has promised will happen by 2017, is going to be one of the main topics discussed by the advisory group, alongside other issues including boosting productivity and building new houses.
The meetings will be chaired by the prime minister and will also be attended by chancellor George Osborne and business secretary Sajid Javid.