Butcher has already held talks with Easter Road chairman Rod Petrie on Wednesday after being given permission to discuss the position vacated by Pat Fenlon last week.
The former England captain has not travelled with the Caley Thistle squad for their Scottish Premiership clash with Hibs today and his assistant Maurice Malpas will take charge of the visitors.
In almost five years in the Highlands Butcher has taken Caley Thistle to the brink of European football, and recently led his charges to a second successive League Cup semi-final.
Mike Reilly from the Hibernian Supporters Association believes Butcher's arrival will go down well with the long-suffering Hibernian supporters.
"I think the fans are quite happy that it's Terry that's coming there," Reilly said on Sky Sports News.
"If he can do the job that he's done at Inverness, if he can bring that to Easter Road, then we would be delighted.
"If he comes and does a good job and gets the best out of all the Hibs players then I don't see any reason why we can't finish very high up the league.
"I'm sure Rod Petrie's done his homework again and he'll probably think he's got the best man, and we all hope he has."