The 30-year-old has been rewarded for an impressive run earlier this season when Pepe Reina was injured.
Ten of his 14 Liverpool games have come this term, though his highest-profile appearance was in last season's FA Cup semi-final victory over Everton.
Brendan Rodgers has now secured the futures of several senior squad members since succeeding Kenny Dalglish.
Jones is confident his new contract has shown he has proved himself to Rodgers after initial doubts over his future at the club.
The Australia international said: "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.
"He was very honest with me at the start and said maybe things weren't going
to work out.
"But he was then just as honest to come and say to me I'd done well and proved myself to him.
"That's what you want from your manager - somebody that's honest, that you can talk to and is going to help you progress as a player.
"He's a big influence. He's a very positive guy and somebody that wants to be
amongst the players, talking to them and making sure they know what he wants.
"I'm happy to stay on and happy the club have been supportive with me and I've seen enough to want to keep me here longer."
A week ago Rodgers moved to dismiss speculation he was preparing to bring in a new goalkeeper in the January transfer window.
The Reds boss had been linked with moves for Birmingham's England goalkeeper Jack Butland and young German prospect Ron-Robert Zieler.
That led to suggestions Reina's future was in doubt but Rodgers rejected that notion, insisting he was very happy with the two goalkeepers he had.
"Of course you are always looking for talent but what we have is one of the best number one keepers in the Premier League in Pepe Reina and then Brad Jones, who was a number three or number four keeper here but has really kicked on since the summer," Rodgers said at the time.
"In the games Brad has played he's showed he is a very loyal and supportive number two. Our job then below that is to ensure we have top young talents who can then hopefully challenge at the top end."
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