He is their most decorated individual, with four Premier League titles, one Champions League, five FA Cups, a Europa League and three League Cups.
He has made 713 Chelsea appearances since his 1998 debut - 578 as captain.
"I feel I still have plenty to offer on the pitch but understand that opportunities here at Chelsea will be limited for me," Terry, 36, said.
Centre-back Terry, who has scored 66 goals for the club he joined as a 14-year-old, has made just four Premier League starts this season.
He is the club's third highest all-time appearance maker, behind Ron Harris and Peter Bonetti, and holds the club record for appearances as captain.
'I will always be a Blue'
Terry, who made his debut for Chelsea as a 17-year-old in a 1998 League Cup match, has gone on to score 40 Premier League goals over 19 years.
He has played almost all of his career at Chelsea, other than six loan appearances for Nottingham Forest in 2000.
John Terry was banned for the 2012 Champions League final, when Chelsea lifted the trophy
"I will, of course, always be a Blue and am desperate to end my final season as a Chelsea player with more silverware," said Terry, whose team have a four-point lead at the top of the Premier League table.
"I've always been conscious that I depart at the right time, in the right way, and I feel that the end of this season is the right time for the club and I."
Terry, the club and Premier League's top-scoring defender, is one of just five defenders to have won the PFA Player of the Year award.
He retired from international football in 2012 after winning 78 England caps and signed a one-year contract extension with the Blues in May 2016.
"I'm eager to carry on playing and so will be looking to continue with a new challenge," Terry added.
"Words cannot describe the love I have for our football club and our amazing Chelsea fans. You mean the world to me and I will never forget the incredible journey we've been on."
Chelsea director Marina Granovskaia said: "He will always be held in the highest regard by everybody at Stamford Bridge and we look forward to welcoming him back in the future."
Terry's highs and lows
Terry made his debut as a 17-year-old against Aston Villa in the League Cup in October 1998, and scored his first goal for the club in an FA Cup sixth-round tie against Gillingham in 2000.
However, the following year Terry was one of four Chelsea players fined two weeks' wages by the club following their behaviour at a hotel in the aftermath of the September 11 attacks in the United States.
He was integral to the Blues claiming both the Premier League title and the FA Cup in 2009-10, making more than 50 appearances as Chelsea became just the seventh club to do the double.
However, he was twice stripped of the England captaincy, before being banned for four matches and fined £220,000 for racially abusing QPR defender Anton Ferdinand, meaning he missed the Champions League final where the Blues lifted the trophy.
He recovered to score four goals in 35 league appearances as Chelsea claimed the Premier League title in 2014-15, but has found his playing time limited under Antonio Conte.