The 24-year-old, who came through Norwich's youth system, made 43 appearances for the U's last season.
Barnet head coach Rossi Eames said:  "It's a fantastic coup for the club as he's got vast experience.
"He was part of an excellent side at Colchester and he's going to bring athleticism, technical and tactical abilities to our back line."
The defender also had a two-year spell at Rotherham and helped them win promotion to the Championship in 2014.
The Bees have not revealed the length of Brindley's contract.
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Barnet have signed right-back Richard Brindley on a free transfer after he was released by Colchester.