Burton will succeed Leonard Goldberg, who is stepping down from the role, but remaining a member of the company’s board of directors.
Burton was previously CEO of SAC Re, where he saw the company through from its inception to its sale to the Hamilton Insurance Group.
Before this, worked at Lancashire Group, holding several roles including deputy CEO and CEO of the group’s Bermuda subsidiary.
David Einhorn, chairman of the board of directors of Greenlight Re, said: “Following a comprehensive search process, we identified Simon as the clear choice to bring Greenlight Re to its next phase of growth.”
Burton said: “Greenlight Re has tremendous talent and an excellent platform. I am looking forward to leading the company to profitably grow the business and help maximise shareholder value over the long term.”