The Australian’s decision – with 100 days to go until the Olympics – came hours after he was suspended by British Cycling, pending an independent probe into the claims amid pressure from funding body UK Sport.
Sutton, 58, was accused by British cyclist Jess Varnish of telling her to “move on and go and have a baby” after she was dropped from the Olympic team for this summer’s Games in Rio.
It has also been alleged he referred to para-cyclists as “wobblies”.
“The developments over the past few days have clearly become a distraction. It is for this reason, and having spoken to friends and family, that I believe it is in the best interests of British Cycling for me to step down from my position as technical director,” said Sutton.
“It is important that the review announced by British Cycling and UK Sport now takes place, and I will obviously co-operate fully with this. I have made clear that I reject the specific claims that have been made against me in recent days, and I look forward to taking a full part in the review process so I can respond to the allegations in detail.”
Sutton worked as head coach for British Cycling under performance director Sir Dave Brailsford and was promoted on his departure in 2014.
“I want to put on record my thanks to Shane for his work with British Cycling and the part he has played in our success,” said chief executive Ian Drake.
“We have a lot to be proud of and, with the Olympics and Paralympics this summer, a lot to look forward to. I understand and respect Shane’s decision to stand down. His primary focus has always been the athletes, and this decision is something he has taken to allow them to focus on their preparation for Rio.”
Sutton is also a shareholder in and consultant to Athlete Lab, an indoor cycling business which boasts of teaching the Shane Sutton Method and whose only UK branch is on Cannon Street in the City of London.
Athlete Lab has not responded to requests for comment from City A.M.