Gourlay, 46, has been with the west London club for five years in a variety of roles and was previously chief operating officer.
Before that, he had senior roles at Manchester United and sportswear maker Umbro.
"Ron was the outstanding candidate for the job," said chairman Bruce Buck. "It was not necessary to look outside as we had someone with all the necessary attributes inside which was important as it ensures continuity and a smooth transition.
"He has the total support of the board and Roman (Abramovich) and both the football and business elements of the club will report to him."
Chelsea said on Wednesday that Kenyon would leave his post on October 31 but continue to serve as a non-executive director and represent the club on various UEFA and European Clubs' Association committees.
