Mr Kelvin, 64, who has denied allegations of inappropriate conduct against him, will now have a nominated director on the board to represent his interests.
He founded the company in 1988, but took leave of absence immediately after harassment allegations were published in the Sunday Times in 2018.
Then, the executive chair of the company, David Bernstein, praised Mr Kelvin “for his tireless energy and vision”.
But he added that “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”.
An independent investigation into the allegations was conducted by City law firm Herbert Smith Freehills.