Roberts, who failed to agree a new contract with Huddersfield at the end of the season, has put pen to paper on a two-year deal at the County Ground.
The 28-year-old, Swindon boss Paolo Di Canio's third summer signing following the arrival of James Collins and Andy Williams on Monday, made over 160 appearances for Huddersfield after signing for an undisclosed fee from Ipswich in the summer of 2008.
He made 45 appearances for the Terriers as they secured promotion to the npower Championship via the play-offs last season and scored seven goals.
Roberts began his career at Crewe and spent almost two years at Accrington before signing for Ipswich for an undisclosed fee in January 2007 following an initial loan spell.
