She succeeds Andrew Lynch who will stand down after nine years in the role.
Swann has had a 23 year career in the retail industry and was CEO of WHSmith for ten years until July 1.
Kate Swann said, 'I am delighted to be joining SSP and look forward to working with the team as we continue to grow the business and deliver for our customers'.
Lynch said, 'I feel privileged to have had the opportunity to lead SSP for a long and exciting period and I am proud to leave it in good shape, with a strong track record of sales and profit growth, an exciting pipeline, and an excellent management team'.
SSP Chairman, Vagn Soerensen, said, 'Andrew has done a great job in building SSP into an international market leader in its sector. The strength of both the management team and brand portfolio leaves the business very well-positioned for further growth. We wish him every success in the future. I very much look forward to working with Kate to continue developing SSP in the years to come. SSP will benefit from Kate’s vast retail experience from WHSmith in accelerating growth and working with business partners, while continuously improving the customer experience'.