The centre-back, who played alongside manager Monk at the heart of the Swansea defence during his early seasons at the club, had been linked with moves to the likes of Sunderland and Napoli, with his old deal set to run out next summer.
However, Williams - captain at both club and international level with Wales - committed his future to the Liberty Stadium outfit on Friday, signing a contract that keeps him in Swansea until 2018.
And Monk was delighted to have finally put a stop to the rumours surrounding his skipper.
"He's an important player to us, and he's captain of this club and country," he told the club's official website. "I've got a good relationship with Ash and he represents a lot of the values that this club stands for. It’s important that we keep players like that around.
"It's key that you have someone like that. He understands the way I want to work to take the club forward.
"He wants to be part of that and he buys into that way of working. He’s a great guy to implement that through to the players.
"He was definitely one of the biggest signings we could have made."
Williams joined Swansea from Stockport County in 2008 - initially on loan - and took over from Monk as club captain in 2013.
"In my conversations with Ashley it was clear he wanted to be here, and now his contract is sorted he can concentrate on his football," added Monk. "He's an excellent player. He’s aggressive, a very good defender on the floor, an organiser, a leader and he can pass the ball with both feet.
"He's a big part of this team."
