Fitch is to depart in April to become head of communications at Lloyd's of London.
He has been at the DWP since 2007, joining from his role as associate director at Fishburn Hedges.
Fitch said: 'It has been a privilege to work at the DWP. It's a department that delivers to millions of people every day and has really stepped up to meet the challenge of the recession. Communications has underpinned that delivery and I'm leaving behind a great team. It has taken a special opportunity to tempt me away.'
His replacement is exppected to continue the DWP's work aimed at helping people find jobs and informing the public about pension reforms.
Fitch has also worked at the London Mayor's office, where he led the transport and environment team as senior press officer.
Fitch, who will oversee about 30 staff in his Lloyd's role, added: 'I'm excited to be joining a famous name with an international reach.
'There's an interesting job to do in terms of differentiating Lloyd's continued success from the banking crisis, protecting the brand and helping the business grow worldwide.'