The career civil servant has left to become head of strategy in the Prime Minister's Strategic Comms Unit at Number 10.
Head of strategy and marketing Anne Nash is filling in for Simpson until a permanent replacement is recruited.
The incoming Home Office comms director will have to grapple with manifold controversial issues including terrorism, immigration, anti-social behaviour and the shortage of places in prisons. The postholder will report to permanent secretary David Normington and will work closely with Home Secretary John Reid.
Simpson now reports to permanent secretary for government comms Howell James and works alongside the PM's official spokesman Tom Kelly. She takes up a role previously occupied by Huw Evans, who has joined Royal Bank of Scotland.
Simpson was previously at the Department for Education and Employment. Before Whitehall, Simpson worked for Camden Council in London.