Peden had been head coach since 2013 and guided the men's sprint team to unparalleled success.
It netted nine world medals, an Olympic silver medal at Rio and 14 Commonwealth Games medals, including back-to-back golds in team and individual sprint.
Despite that success, Peden felt his approach did not align with Cycling New Zealand's.
He felt it was the right time to move on to allow a new coach time to prepare the team for the Tokyo Olympics.
''I love all the athletes in the sprint programme. They have given me everything that I have asked of them,'' Peden said.
''I have put plans and processes in place through to Tokyo and I truly believe that these athletes will be successful in 2020.
''This is one of the hardest decisions I have made and, while I am proud of what we have achieved here, it is the best thing for me to step away.
''I intend to remain in the sport and believe there are some exciting prospects ahead.''
Cycling New Zealand CEO Andrew Matheson said his organisation had lost a coach of high quality and his sprint group was the talisman for the programme.
''The results speak for themselves, with Anthony having been a Halberg Award coach of the year and his sprinters have achieved global success.
''We understand and respect Anthony's decision, as he does with our position.
''He will leave with things in an organised state. We've already spoken to all of the sprinters in the programme and put in place a short-term fix while we look to advertise this role.
''Anthony has built a world-class programme and there is some depth looking forward, so I expect there to be considerable interest in the role.''
