The former Inverness Caledonian Thistle boss emerged as a target for Hibernian last week following the departure of Pat Fenlon, and compensation between the clubs was agreed on Monday.
Inverness recorded a 2-0 win at Easter Road on Saturday and sit second in the Scottish Premiership on 20 points.
However, Butcher and his assistant Maurice Malpas - who took charge against Hibernian - have now moved to the club sitting seventh in the table after agreeing personal terms
Butcher's first assignment as Hibernian boss will be an away clash at St Mirren on November 23, when he will hope to end his new club's four-match winless run.
"I'm excited about the future and what we can achieve at Hibernian - it's a great honour to be appointed the new manager of the club," Butcher told the club's website.
"I've been really impressed with the set-up; from the training facilities 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 and to implement a winning mindset.
"This is a big football club with big expectations, but with energy, enthusiasm, desire and focus I believe we can rise to the challenge ahead and win."
Chairman Rod Petrie declared his delight at having secured the former England international.
"Terry is vastly experienced in Scottish football and an outstanding leader of men," said Petrie.
"He inherits a talented squad of players and we believe he has got the managerial skills and motivational qualities required to develop them as players and as a team and move the club forward."
