Evans spent 3 years at the County Ground after joining from Chelsea where he had been a England Under 21 goalkeeper, and last year he was named as Swindon's player of the season.
Evans said: "The only delay was sorting out my future at Swindon. Being a Swindon person I thought it was only right to show a little bit of respect to them.
"It is disappointing the way things have turned out but hopefully I can become a success with Blackpool now."