Butcher, who will be joined by former Caley assistant Maurice Malpas at Easter Road, has signed a three-year contract.
The 54-year-old, who had previous spells in charge of Motherwell, Coventry and Sunderland, said it was a 'huge honour to be taking over a club like Hibernian'.
Speaking on the club's official website, he said: "I am excited about the future and what we can achieve at Hibernian.
"It is a great honour to be appointed the manager of the club. I have been really impressed by the set-up, from the training ground right through to the stadium.
"Everything is in place and now our goal is to deliver the success on the pitch that everybody wants.
"We want everybody associated with Hibernian - players, staff and supporters - to all pull in the same direction to implement a winning mindset.
"This is a big football club with big expectations and with energy, enthusiasm, desire and focus and I believe we can rise to the challenges ahead."
On leaving Inverness after almost five years, having led them to second in the table and a second successive League Cup semi-final, Butcher said: "It has been a very difficult week for us because of what we have left behind up there.
"We have left some fabulous players and it was hard to say goodbye to that. If you look at the way Caley Thistle played last Saturday then that is the sort of way we want to get Hibs playing from now on.
"It was great to be at the training centre today. The players are terrific and wanted to impress us and we are just delighted to be here."
Hibs chairman Rod Petrie, who agreed a compensation deal with Inverness to secure the services of Butcher and Malpas, said: "Terry is vastly experienced in Scottish football and is a great leader of men.
"He inherits a talented squad of players and we believe he has the managerial skills and motivational qualities required to develop them as players and as a team and to move the club forward."
Butcher takes over the club, who currently sit seventh in the SPFL table, from former boss Pat Fenlon who quit on November 1 in the wake of a derby defeat by city rivals Hearts.
You can see how Butcher fares in his first match in charge of Hibs against St Mirren live on Sky Sports 3 from 12.45pm on Saturday, November 23