Doncaster born Butler, 30 and Basham, 25 become the Blades fourth signing of the summer following the arrivals of Marc McNulty (Livingston) and Jamal Campbell-Ryce (Nott's County).
Both players arrive on a free transfer following the end of their contracts at Bescot Stadium and Bloomfield Road. Butler has put pen to paper on a two year deal whilst Basham has signed for three years.