Oliver Holt of the Daily Mirror reports Terry wanted a longer commitment from the Blues, but his desire to remain with the club led him to sign a short-term deal:
There was interest from clubs abroad but Jose Mourinho was desperate to hang on to Terry.
Terry has only ever played for Chelsea and is keen to add another league title to his haul before the end of his career.
Chelsea later confirmed the extension on the club website:
Speaking after completing his new deal, Terry said: "I'm delighted to have signed an extension to my contract with Chelsea taking me into my 20th year with the club.
"I'd like to thank the fans and club for their continued support, and the Manager who was instrumental for me the last season."
Chief Executive Ron Gourlay added: "We are very pleased John, who is an undoubted Chelsea legend, will continue to lead the team next season, as he has done for so many years with unrivalled achievement.
"Both Chelsea FC and John have been clear throughout that we wanted his outstanding career at the club to continue, and it is important the matter has been concluded so soon after the end of the season, allowing us to look forward to and plan for 2014/15."
Terry is coming off another strong season in the middle of the Chelsea back line. He appeared in 47 matches across all competitions. It continued a trend of success that began shortly after the longtime England international joined the Blues in 1998.
The captain completed better than 90 percent of his passes and won nearly three aerial duels per game across Premier League and Champions League play, according to WhoScored.com. He chipped in two goals and an assist in those matches.
Although Terry would have drawn interest from numerous clubs if a new Chelsea deal wasn't reached, he worked to make sure it didn't reach that point. ESPN passed along comments from the defender last month, who said he hoped to end his career with the Blues:
Clearly, I want to stay for the rest of my footballing days.
At the minute we're in talks and it's ongoing. I'm hoping it gets done. It's down to the club. They know I want to stay.
A one-year deal obviously doesn't go all the way to ensure that will be the case. It's another step in the right direction, though. It also gives the sides another season to work on a contract that could do more to make certain he won't conclude his storied career elsewhere.
As long as he continues to showcase solid form, it wouldn't make sense for Chelsea to let him get away. Not only is he a stalwart at the back, helping the club allow 10 fewer goals than any other in Premier League play, but he can also move forward as a weapon, especially on set pieces.
WhoScored.com noted his aerial success in the attacking third:
At 33, it's unclear how many more seasons Terry can go before showing signs of reduced top-end form. That's probably one of the main reasons Chelsea weren't ready to commit beyond one year. However, at least in the short term, he should remain a vital part of the club.
By locking him up for another year early in the offseason, the Blues can allocate more time and resources to finding players who can help the attack next season. Given the strength at the back, even marginal improvement offensively would be a major boost to their title chances.
Terry is still a key piece of that championship puzzle.