The 35-year-old had been hoping to secure a 12-month extension but was informed by the club of their decision prior to last week's win at Arsenal.
And the former England captain made Chelsea's decision public in a hotel corridor inside stadium:mk following a 5-1 FA Cup win at MK Dons on Sunday.
"It's not going to be a fairytale ending, I'm not going to retire at Chelsea," Terry said.
Terry said the incoming manager may be able to reverse the decision, while Chelsea suggested a contract offer could be forthcoming.
A club spokesman said: "John requested a meeting with the club the week before last.
"In that meeting he asked about the possibility of an extension to his existing contract.
"John was advised that while no new deal was currently on the table, that situation could change in the coming months.
"The club has the utmost respect for John and everything he has helped us achieve to date.
"He is a fantastic servant of Chelsea Football Club and a superb captain and, as such, the club will keep the channels of dialogue open."
It seems the end of Terry's Chelsea career is nigh, unless some major repair works can be done.
He joined Chelsea at the age of 14 and has since made 696 appearances, scoring 66 goals, during 18 seasons as a first-team player.
He has won every major club honour with the Blues, including the Champions League in 2012, four Premier League titles, five FA Cups, three League Cups and the 2013 Europa League.
Chelsea have endured a season of struggle, with Jose Mourinho leaving for the second time in December, and now their talismanic skipper has announced he will be moving on, unless there is a change of heart.
He is yet to decide where, except outside of England, and big-money offers are likely to come in from Major League Soccer and the Chinese Super League.
Terry added: "Ideally I would have loved to stay, but the club's moving in a different direction.
"My agent made the call like we do every January
He got told over the phone and I called to set up a meeting the following day.
"I wanted to hear it face to face
They told me
Unfortunately it's not going to be.
"They said that when the new manager comes in, things might change
It's a no at the minute
It took me a couple of days to get over."
Terry's career has been punctuated by controversies and he is a divisive figure in the game, but not at Chelsea, where he is adored by the supporters.
He was a pivotal figure in the Blues' first Premier League title in five years, playing every minute of all 38 games.
But his star has since waned and in the second Premier League game of this season, at Manchester City, he was substituted at half-time in a 3-0 loss.
Terry was not the automatic choice he had been in Mourinho's first spell thereafter.
He came out in support of the Portuguese, denying speculation of a falling-out, before Mourinho was sacked in December.
Terry's season high point so far was a controversial late goal against Everton two weeks ago.
He was offside when he scored eight minutes into stoppage time to earn a 3-3 draw.
Afterwards Terry spoke of his desire to stay on at Chelsea, while interim boss Guus Hiddink sang his praises.
Terry will hope to finish with another FA Cup winners' medal, but Chelsea must first face Manchester City in the fifth round.
The Blues cantered to victory at MK Dons, with Oscar scoring a first half hat-trick and Eden Hazard ending a 31-game goal drought.
Bertrand Traore, whose recruitment by Chelsea is under scrutiny, added a fifth.
Source : PA
Source: PA