Elstone, 54, is leaving Goodison Park after 13 years to become the Betfred Super League’s new chief executive, filling the role created by the departure of Roger Draper in January.
There has been no confirmation from the Rugby Football League but Everton chairman Bill Kenwright announced on his club’s website that Elstone would be returning to rugby league and wished him well leading his favourite sport.
The Barnsley-born Castleford fan was deputy to chief executive Maurice Lindsay at the RFL in the 1990s and, after helping him launch the era of Super League, was earmarked as his successor.
But Elstone, who also worked for Sports Business Group Deloitte, moved to Everton in 2005, initially as deputy chief executive and three years later was promoted into the hot seat.
The role of RFL chief executive, for which he was destined as a young man, remains vacant following the departure of Nigel Wood but the Super League job is now arguably more influential following last November’s special general meeting at which the clubs seized more power from the executive.
Those clubs have now turned to Elstone to lead negotiations on a new television deal and potential re-structuring of the domestic competition.
Despite his deep involvement in football, Elstone has remained a passionate rugby league fan.
A former board member of Castleford, it did not go unnoticed that Elstone opted to watch the Tigers’ play-off semi-final against St Helens last September rather than Everton’s opening Europa League clash with Apollon Limassol and he was at the Jungle last Saturday to witness his team’s Challenge Cup defeat by Saints.
Kenwright said: “We are sad to see Robert leave the club and wish him nothing but success.
“Robert has obviously been a passionate Evertonian since the day he first set foot here but I have always known that his enduring love has been rugby league.
“And we wish him well in his new role leading his favourite sport.
“Robert has run the club wisely and well, throughout his time as our chief executive, and has become one of the most respected in the game.
“I will personally miss him for all the help he gave me, particularly on difficult transfer negotiations - and for the stability he brought to the club throughout his time here.”
Elstone, who will be succeeded as chief executive by professor Denise Barrett-Baxendale from 1 June, said: “I have enjoyed 13 wonderful years here and feel privileged to have been able to play a significant role in the development of such a great club.
“I will leave with many great memories, all shared with fantastic and talented colleagues.”