Kelly joins from BAA, where he has been director of communications since 2007.
A former BBC journalist, his previous civil service roles include communications director at the Northern Ireland Office and Prime Minister’s official spokesman, where he worked from 2001 to 2007.
He will take up his new role on May 4 and will report to FSA chief executive Hector Sants.
Sants says: “I am pleased to welcome Tom Kelly to the FSA’s senior management team. His breadth of communications experience will bring considerable strength to the organisation as we take forward the priorities we have laid out in our recent business plan.”