Butcher replaced Pat Fenlon in November but after a disastrous run of form, which saw the Leith side win just once in their last 18 league games, his side were relegated after a penalty shoot-out loss to Hamilton in the Scottish Premiership play-off final.
The former England captain met with new Hibs chief executive Leeann Dempster and chairman Rod Petrie on Monday for make-or-break talks but 24 hours later the club announced they had relieved the 55-year-old of his duties.
Hibs claim the decision to sack the former Motherwell, Brentford and Inverness boss was "unanimously agreed" by the Easter Road board.
Dempster will now lead the search for the club's third manager in under a year.
She said: "I have to say that we all regret that this decision had to be made, but during conversation it became clear that a different approach was needed.
"Sadly, for a variety of reasons and perhaps including unfortunate timing, it hasn't worked out for Terry here. That is disappointing for all concerned. I am genuinely saddened that we have had to take this tough decision.
"It may have taken longer than we all would have liked but I felt it was appropriate that we met properly and had a full discussion before any decision was made.
"Now we need to move forward and act to bring in a new manager with the aim of getting us promoted back to where Hibernian belongs, in the top league of Scottish football, from a uniquely competitive Championship.
"Our first aim must be to try to win the league and gain promotion automatically.
"The search now begins to find and appoint the next manager, and while we will try to keep supporters updated regarding the process as much as we can, I know they will understand that we need to be professional in all that we do.
"Unfortunately assistant manager Maurice Malpas is abroad on holiday at present and I want to meet him on his return to explain the situation at the club."
Butcher was hired to clear up the mess created by Fenlon's disastrous last three months in charge.
He took over a side in seventh place in the top-flight on November 12 and initially, results were positive with four wins from his first seven games in charge.
The last of those was 2-1 derby success over Edinburgh rivals Hearts - their first against the administration-hit Jambos in three attempts - but instead of building on that victory, Hibs nosedived.
They would win only one more regular-season league clash - a 2-1 home win over Ross County in February - before a last-day defeat to Kilmarnock consigned them to the play-offs.
But despite taking a 2-0 first-leg lead at New Douglas Park, the top-flight side look petrified of their second-tier opponents.
Jason Scotland handed Accies an early lead early on in the Leith return before Tony Andreu sent the tie into extra-time with a 93rd-minute equaliser.
Kevin Thomson and Jason Cummings' missed spot-kicks in the shoot-out decided ultimately cost the Edinburgh side, who will now play Championship football next season for the first time in 15 years.
The day after their play-off defeat, Butcher released a swathe of players but former skipper James McPake - one of 15 players allowed to leave - insisted the first-team squad were not the only ones to blame.
The 29-year-old - who did not feature during the relegation run in, despite insisting he was fit to play after a back injury - said at the time: "There is no way that relegation is entirely the players' fault.
"I was told that I am not part of the manager's plans and I'm gutted about it.
"I am disappointed I did not get the chance to help us stay in the Premiership.
"I was 100 per cent fit and could have been contributing but the manager said he believed I wasn't fit enough.
"That's his opinion, it's not an opinion I agree with."