Wheeldon joins the LSE next month with a remit to tackle a number of approaching public policy issues in the UK and Brussels.
He leaves Luther Pendragon after two-and-a-half years to take the role, which will also see him join the LSE management team and working closely with CEO Clara Furse.
LSE director of comms Nick Gammage said: 'We face a range of public policy issues that are coming out affecting the financial services sector, for example directives coming out of Brussels. We are putting more focus on strategic and tactical communications in Whitehall and Brussels.'
Wheeldon said: 'I'm going to be looking at how we can be as effective as possible in communicating and getting messages across to key audiences in Whitehall and Europe.'
News of his appointment follows a recent malicious whispering campaign against Furse, over which the LSE threatened to sue.