Butcher was targeted by Hibernian last week following the departure of Pat Fenlon and watched from the stands as Inverness recorded a 2-0 win at Easter Road on Saturday.
Despite that success, Butcher and his assistant Maurice Malpas, who took charge against Hibernian at the weekend, have expressed a desire to leave Inverness and their wish now looks set to be granted, providing personal terms can be agreed.
In a statement, Hibernian chairman Rod Petrie said: "We are grateful to Inverness Caledonian Thistle for the professional and courteous way in which the discussions between the clubs have been conducted. We now look forward to welcoming the new management team to Easter Road Stadium."
Inverness sit second in the Scottish Premiership – 10 points clear of Hibernian – and expressed understandable regret at the imminent exit of their managerial team, while also revealing Malpas had been offered the opportunity to succeed Butcher.
"It is a major disappointment to the club and the supporters that they have taken this decision," said chairman Kenny Cameron.
"I'd like to put on record our appreciation of the excellent job they have done at Inverness since Caley Thistle provided them with the opportunity to join the club in January 2009.
"Maurice was offered the manager's role but declined. We would, however, like to record our sincere appreciation to him for taking the team on Saturday in what was a resounding victory.
"This is the fourth time that Caley Thistle have found themselves in the situation of having their manager head-hunted by another Scottish Premier club, with Steve Paterson, John Robertson and Craig Brewster being the other instances.
"What it does show is that Caley Thistle have a tradition of getting their selection process right and the club has continued to progress. It is our aspiration to maintain this sequence."
