Mr Kelvin, who also founded the retailer, was forced to take a leave of absence last year amid claims that he enforced a “hugging” culture at the company.
Accusations were also made that he massaged employees, kissed their ears and asked some to sit on his lap.
Mr Kelvin denies all allegations of misconduct, but Ted Baker said on Monday that he agreed to resign as chief executive and director of the retail chain.
Executive chairman David Bernstein said: “Ray Kelvin founded the business 32 years ago and has, together with the fantastic team around him, been the driving force behind it becoming the global brand it is today.
“As founder and CEO, we are grateful for his tireless energy and vision. However, in light of the allegations made against him, Ray has decided that it is in the best interests of the company for him to resign so that the business can move forward under new leadership.”
Mr Kelvin himself said that stepping away is the “right thing to do”.
He said: “The past few months have been deeply distressing and I’ll now be taking time privately with my family to consider what my next adventure will be. Bye for now, Ray.”
An internal independent committee has been in the process of investigating the allegations alongside law firm Herbert Smith Freehills.
The probe will continue, with the primary focus now on Ted Baker’s policies, procedures and handling of complaints.
Acting chief executive Lindsay Page has agreed to continue in the role, with Mr Bernstein providing additional support in an executive capacity until no later than November 30 2020, by which time a successor will be appointed.
Mr Bernstein added: “As a board of directors, we are committed to ensuring that all employees feel respected and valued. We are determined to learn lessons from what has happened and from what our employees have told us and to ensure that, while the many positive and unique aspects of Ted’s culture are maintained, appropriate changes are made.”
“Sharon Baylay has agreed to act as the designated non-executive director for engagement with the Ted workforce. Led by Lindsay, we are confident that the strong and experienced team we have in place will build the Ted culture and move the business forward.”