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.
Find all the latest football transfers on our dedicated page.

Eubank Jr, 27, produced a fine display to win by margins of 118-110, 118-110 and 120-108 at Wembley Arena.
It was only the sixth defeat of Abraham's 52-fight career.
Eubank Jr will now take part in the inaugural World Boxing Super Series - an eight-man tournament featuring some of the biggest names in the division.
WBA champion George Groves and fellow Britons Callum Smith and Jamie Cox are also in the competition, which has a $50m (£38m) prize fund.
Eubank Jr will fight Turkey's Avni Yildirim in the Super Series quarter-finals in the autumn, with semi-finals in January and a May final in a tournament which organisers say will "change the world of boxing."
Abraham, 37, has beaten Britain's Paul Smith (twice) and Martin Murray in his career and lost on points to Carl Froch in November 2010.
But the German, who has held world titles at middleweight and super-middleweight, was outclassed by the younger man.
Eubank took his record to 25 wins and one defeat and felt he made "a statement" with the victory. He told ITV Sport: "He's the most durable opponent I've faced. I hit him with every punch in the book.
"I'm happy with the performance. I got to show my skills, I got to go the 12 rounds and get the experience in."
His father, Chris Eubank Sr, a former two-weight world champion, added: "I believe he's the best in the world. Over the coming nine months, he will be able to clean the slate and come away with the Muhammad Ali Trophy and all the belts."
On the undercard, Wales' Lee Selby retained his IBF world featherweight title with a unanimous points win over Argentina's Jonathan Victor Barros.
Selby, 30, knocked the Argentine down in the last round before getting a wide verdict, with one judge scoring it 119-108 and two marking it as 117-110.
In the featherweight division, Sheffield-based Kid Galahad maintained his unbeaten record with a 10th-round stoppage of Mexican Jose Cayetano.
Galahad, 27, has now won all 22 of his professional bouts and this victory saw him collect the vacant IBF Inter-Continental title.
Liverpool's Robbie Davies Jr suffered his first professional defeat in 16 contests as he was stopped in the last round of his super-lightweight bout with Poland's Michal Syrowatka.
Martin Joseph Ward held on to his British super-featherweight belt and also gained the Commonwealth title with a unanimous points win over previously undefeated Anthony Cacace.
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Barnet have signed right-back Richard Brindley on a free transfer after he was released by Colchester.
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Chris Eubank Jr retained his IBO world super-middleweight title by beating former two-weight world champion Arthur Abraham with a unanimous points win.