Fitch has worked for almost four years at the insurance market after a stint as head of news at the Department for Work and Pensions.
He started his career as a journalist before spending time in Mayor Livingstone’s comms team and at agency Fishburn Hedges.
Blue Rubicon CEO Gordon Tempest-Hay said: "Peter has vast experience he will bring to bear as we grow our strategic communications business. Often people will have a great in-house record, or a great agency record, but there are very few people who have done it all. Peter is one of those and combines senior government experience with major corporate experience."
Fitch has worked closely with Lloyd’s of London CEO Richard Ward, who is due to step down at the end of the year.
Tempest-Hay added: "In almost all of what he has done, Peter has been counselling very senior clients. More and more of what we’re doing is working with the C-suite, and it’s about having people who are comfortable in that environment."
Earlier this month, it emerged that Blue Rubicon’s Spencer Livermore is returning to the Labour Party as campaign director ahead of the 2015 election.