Britton, 29, still had a year remaining on his existing deal, but manager Brendan Rodgers was keen to tie the playmaker to a longer contract after watching him turn in a string of fine performances in Swansea's maiden Barclays Premier League campaign.
Britton told the club's official website: "I'm pleased to complete the deal. It was an easy decision for me to make, although I still find it strange when I look back to the day I left for Sheffield United. I didn't even think I would be back in Swansea colours, let alone playing for the club in the Premier League armed with a new three-year contract."
He continued: "This deal will take me up to my 32nd birthday, but I'd like to think if I can keep myself fit and healthy, live my life right, then I can go on playing until my mid-to-late thirties.
"In an ideal world I would like to stay at Swansea until the day I retire - or they retire me - because I love it here and the club has a bright future ahead of it.
"Our debut season in the Barclays Premier League has gone well so far and everyone wants to build on that. If we all stick together then, like I said, the future is bright."
Britton has won plenty of plaudits this season as a key cog in Swansea's acclaimed possession style. The West Ham product became the first player to record perfect passing statistics in a Premier League game after completing all 67 of his attempted passes in the win over Bolton.
His pass completion rate remains in the low 90s and he has won comparisons with the Barcelona duo Xavi and Andres Iniesta for that statistic, as well as being tipped for an England call-up.
The midfielder joined the Swans on an initial loan from West Ham in 2002, and after making that switch permanent he went on to make 335 appearances before moving to Sheffield United in 2010.
But Britton returned to the Liberty Stadium just six months later, going on to help the club secure promotion via the Championship play-offs.
Source: PA
Source: PA