Lundie, due to start on 20 April, will report to Stephen Doherty, MD of the corporate comms division at Barclays.
Lundie joins Barclays after a 12-year stint at Edelman, where he led a 60-strong team focusing on strategic comms, issues management and corporate strategy.
Before this, he spent seven years as a senior political adviser to Paddy Ashdown and Charles Kennedy while they served as leaders of the Liberal Democrats.
In 2010, The Telegraph revealed that Lundie had been caught up in the MPs' expenses scandal.
David Laws, then chief secretary to the Treasury, had claimed £40,000 in expenses between 2006 and 2009 to sub-let a room in a London property, which was owned by his partner, Lundie.
After resigning from the coalition Cabinet, Laws said he deeply regretted claiming the expenses and vowed to pay back the money.