The left-back, who had his contract with Blues cancelled by mutual consent back in March, had spent the latter part of the season on a short-term contract with Peterborough Utd.
Williams, who made just four first team appearances during his two years at St Andrews, had spent three months on loan at London Road prior to signing for Barry Fry's side where he made 25 appearances during his five months stay.
He joins Paul Hart's side as a free agent.