Monk joined the Swans seven years ago from Barnsley, and has played in all four divisions for the club on their journey from League Two to the Premier League.
Monk told the club website, www.swanseacity.net: "It's a big thing for me to sign a contract that will take me up to my 10th year."
He added: "It's something I am very proud of, my family is proud of, and I've worked hard for it.
"It's a great feeling knowing I can represent the club another three years at least."
The 32-year-old's new deal will keep him with the club until the end of the 2013/14 season, although the former Southampton man has been bedeviled by injuries over the last two seasons.
He recovered from a knee injury in time to lead the Swans to play-off glory at Wembley, and is hopeful of overcoming a foot problem to lead Brendan Rodgers' side in their Premier League opener at Manchester City on Monday.
He added: "Lifting the trophy at Wembley was massive and one of the biggest honours I can have, but every year has been brilliant and filled me with pride. This season will be no different.
"Hopefully I will be back to full fitness as soon as possible. To lead the boys out at Manchester City would be a very proud moment for me.
"We have talked about not just turning up and realising what it's all about after five or six games. We want to be ready from the off. We are playing against fantastic players and fantastic teams, but we have a good squad here and we want to impose our game on the opposition and see how they deal with it."
Source: PA
Source: PA