The 36-year-old has helped GB to win puruit gold at the past three Games and was due to compete in the men’s team pursuit heats on Tuesday, but his place will be taken by Charlie Tanfield following his announcement.
While admitting he was gutted at the way it had ended, Clancy added: “It would be unfair of me to try to carry on now I have aggravated my back injury.
"I want the rest of the lads to build on the hard work we have done and give them the best possible chance of making it on to the podium.
"I will be supporting them all the way.”
Clancy plans on rounding off the season with participation in the UCI Track Champions League, as well as focusing on growing the Clancy Briggs Cycling Academy, but he has expressed a wish to remain in involved with British Cycling.
"I've spent just over 20 years on the Great Britain cycling team and I see it as my family,” he continued.
“I have achieved more during my time than I ever could have dreamed of – it's something I will remember for the rest of my life.
"It's been a pleasure, to the extent that if I could go back in time I would do it all over again.
"It’s a tough call, because I’m enjoying it more now than I ever have done, but the difficult choice is usually the right one.
"I want to thank everyone – family, friends, coaches, trade teams, sponsors, British Cycling and everyone else who has supported me – my career success has been a big team effort.”
As things stand, Clancy is the most successful team pursuit cyclist in Olympic history. He won his first world title in 2005 at the tender age of 20 and retires from Olympic racing with seven under his belt as well as the 2010 omnium title alongside his Games medals.
He helped Britain post their fastest ever time in the men’s team pursuit during qualifying as they finished fourth in 3:47.507.
Stephen Park, Performance Director for British Cycling, said: “I admire Ed for taking the decision to retire from the sport which he still has a strong passion for.
"It was tough for him having to withdraw but his professionalism and honesty led him to make this decision.
“It’s been a pleasure to support Ed with his fantastic achievements and on behalf of everyone on the Great Britain Cycling Team, I wish him the very best of luck for the future, and I hope he keeps some involvement with us.
Six-time Olympic champion and 11-time world title-winner Sir Chris Hoy also paid tribute to Clancy, writing on social media: “The most successful Olympic team pursuiter of all time, and all round top bloke.
"Not the way he wanted to go out, but I hope he is extremely proud of not just what he’s achieved, but also how he achieved it. Enjoy retirement pal.”