Britton turns 34 next month and has made 514 appearances for a club he first joined on loan from West Ham in December 2002.
But the veteran midfielder remains a key part of the Swansea scene and was recently appointed captain following Ashley Williams' departure to Everton.
"Signing the extension was a very easy decision, like most of my contracts at Swansea have been," Britton told the club's website.
"I spoke to the chairman (Huw Jenkins) and said, 'If you are happy to have me, let's just keep the same terms'.
"I think it's one of the easiest contracts the club have ever drawn up.
"If you include the loan deals when I first came, I have now signed 13 contracts at Swansea.
"You never know, there might be a 14th - it's down to me to try to prove I can still do a job."
Britton accepts that his age means he might not remain a first-team choice for manager Francesco Guidolin this season.
But the Londoner remains determined to play as big a part as possible in Swansea's Premier League campaign.
"Looking forward, I know my role will change a little bit in terms of not playing as regularly as I have done over the years," Britton said.
"I have spoken to the manager about that and I understand it.
"I have said to him that I am ready to start, to come on or just to be involved in the squad and trying to help the other players.
"At my age, maybe that sharpness you have when you are 24 or 25 is not there
"You have to adjust your game a bit
You try to read the game better and use your experience
"Getting up to 600 appearances for the club might be a big ask, but you have always got to have targets.
"Getting to 500 was a big thing for me
Now I would say I want to reach 550 and then I will go from there.
"If I can reach 600, that would be great
But I don't think there are too many players who have got to 550, so that would be a great achievement."
Source : PA
Source: PA