The 25-year-old, who rejected the chance to stay in the Championship with the Robins, has agreed a two-year deal at Oakwell.
He said: “It’s been in the pipeline for a few weeks now, I’m happy to get it over the line and I can’t wait to get started.
“First and foremost, I’m a defender. I’m going to win my headers. I like to play out when I can and hopefully, we can do that this season.”
Cundy has spent the last three seasons at Bristol City and finally broke into the first-team picture at Ashton Gate at the end of last season, making 14 appearances.
The former Oxford United trainee, who stands at 6ft 2in, also featured on loan for Torquay, Cambridge United and Gillingham, where he gained League One experience.
He joins goalkeeper Jamie Searle and midfielder Luca Connell as the newest arrivals at Oakwell, along with boss Michael Duff.