Graves is to combine the new role of Yorkshire’s chief executive with that of his current position of club chairman after severing his ties with the Dunnington-based convenience store business.
Graves will start work in his new role at Headingley Carnegie on Monday and be paid a full-time salary by the club.
He sold his shares in Costcutter last November having built the business up from just seven stores in the York area to more than 1,550 across the UK.
“Costcutter wanted me to stay on in a non-executive role and use my name if things went wrong,” said Graves, who has been on the Yorkshire board since 2002.
“But that wasn’t acceptable to me.
“I started that business up from nothing and built it up from scratch.
“I have therefore decided it’s time to move on.”
For more on this story read Saturday’s Yorkshire Post.