Woking opened on Monday 30 September and Stockport will open on Sunday 13 October 2013.
The transformation of the Pumpkin store at Woking station on platform five, and Stockport station between platform one and two, marks a new chapter in SSP's relationship with Starbucks as it continues to open sites in high footfall areas such as airports and railway stations.
All staff from existing Pumpkin branches will transfer to the new Starbuck stores.
Customers visiting the new stores will be able to enjoy what Starbucks believes is the "highest quality Arabica coffee in the world" as well as a range of cakes, pastries, sandwiches and salads.
Mark Angela, chief executive, SSP UK & Ireland, said: "The traveller is at the heart of everything we do to ensure we deliver on our promise of a great experience every time. Starbucks mirrors this philosophy and we're confident that the customers of Woking and Stockport will be delighted with their new stores."
Matt Sikes, VP business development, Starbucks, EMEA, added: "These new sites represent a great opportunity to bring Starbucks to new places. Our customers love our quality coffee and food, and together with SSP we have created unique store environments, which are an unexpected oasis for commuters at Woking and Stockport stations."