Reports in West County say the 25-year-old will undergo a medical with the League One club before signing a three-year deal.
Oxford-born Cundy turned down new terms at Ashton Gate, with his contract due to expire at the end of June.
The 6-foot-2 right-back made a first-team breakthrough at the end of last season, making 14 first-team appearances.
But the lack of regular playing time and the plethora of defensive options at City have forced Cundy to accept that now is the time to move on.
Cundy has spent several loan spells away from City at Exeter, Torquay, Cambridge and Gillingham.
Earlier in his career, he appeared in non-league circles for the likes of Bath City and Gloucester City, having started his career at Oxford United.
Barnsley brought on New Zealand goalkeeper Jamie Searle and former Celtic and Bolton midfielder Luca Connell last week, while his first major game is scheduled to see Cauley Woodrow complete his move to Luton Town shortly.
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Source: www.yorkshirepost.co.uk
This notice was published: 2022-06-21 13:36:17