The 30-year-old enjoyed a run in the first-team during October and November when Pepe Reina was out injured, with the Australian keeping two clean sheets.
Liverpool manager Brendan Rodgers had been linked with a move for Birmingham City’s Jack Butland and Hannover shot stopper Ron-Robert Zieler in recent weeks.
“I’m happy – happy to stay on and happy the club have been supportive with me and seen enough to want to keep me here longer,” Jones told Liverpool’s website.
“I said when I signed here it was a dream come true. It was something I’d wanted as a young boy – and that hasn’t changed. I want to stay here as long as I can.
“At the minute, the club is on a progression and we’re improving a lot. It’s a good time to be here and I’m sure in the next couple of years, I’ll be part of a successful squad.”
Jones also revealed he was concerned about his future at the club when Rodgers replaced Kenny Dalglish in May before the Northern Irishman handed the former Middlesbrough goalkeeper a chance to impress this season.
“He’s a big influence,” added Jones.
“When he came in, I don’t think he was too sure about whether I was going to stay or not and I had to prove to him I was worthy of being here.
“I was happy to get those chances. Obviously they came with Pepe getting injured, but you want to be able to prove you can do it at the top level – and I think in those games, I was able to show I was worthy of being here at least and being in and amongst the squad.”
Jones has made 14 appearances for Liverpool after completing a £3.2m move from Boro in 2010.
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