The 32-year-old joined the Swans on a free transfer from Barnsley in 2004 and has helped the club rise form League Two to the Premier League.
"It's a big thing for me to sign a contract that will take me up to my tenth year," Monk told Swansea's official website. "It's something I'm 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 for another three years at least."
Monk rebuffed bookmaker predictions that Swansea would be relegated after their first season in the top flight, saying the squad intends to be "ready from the off".
"We have talked about not just turning up and realising what it's all about after five or six games," he added. "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."
Swansea kick off their Premier League campaign with an away fixture at Man City next Monday.