Roberts, a Welsh U-19 and U-21 international, has yet to make his first team debut for the Premier League side but made 45 league appearances for Yeovil Town during a season long loan in 2015/16.
Speaking of his latest signing, manager Darrell Clarke said; “I would like to welcome Connor to the club and wish him a successful time with us.
“Connor was a regular in Yeovil’s League Two side last season and can play on the right or left, as a full back or wing back, and will provide competition to Daniel Leadbitter and Lee Brown for either of those places.”
Roberts is a graduate of the Swansea City Academy and signed a one year pro deal with The Swans in 2014 and won the Professional U-21 Development League Two title with the Swansea U-21 side in 2014/15 before signing a new two year contract with the Welsh outfit.
Last season was spent on loan with Yeovil Town and played in all but one of their league games and picked up three Player of the Year Awards for The Glovers.
He made his Welsh U-21 debut against Romania on 29th March this year.