The striker has been linked with a return to Spain and even a switch to Liverpool's rivals Manchester United.
Torres signed a new contract last month and is confident he can satisfy his ambitions on Merseyside.
He told the Daily Mail: "Winning the European Championship with Spain gave me a taste of what winning at the top level was like and once you've had a taste of success it becomes an addiction.
"A lot of players committed themselves to Liverpool this summer with new contracts and players don't do that unless they think they can have their ambitions met.
"There is a lot of belief at the club and a lot of trust in the manager. I sincerely believe I will win the Premier League and the European Cup here. The winning tradition is very clear at Liverpool. I want to be involved in a little piece of their history.
"I'm very happy with my contract at Liverpool and wouldn't leave just to earn a little more somewhere else where I wouldn't be that happy. To want any more would be greedy and that is not me. As long as Liverpool want me, I will stay."
The 25-year-old has been linked with United following their acceptance of Real Madrid's £80 million bid for Cristiano Ronaldo.
Torres will be sad to see the Portuguese leave the Premier League but insists Liverpool will not win the title by default.
"He has been one of the best players in the world for the last three years and it will be a big loss for the league but, with the amount of investment in the Premier League, I expect world-class players to arrive this summer as well," he said.
"Madrid obviously are spending lots of money and I'm sure that (United boss) Sir Alex Ferguson will be looking for a big name to replace Ronaldo, but I'm very excited about what the boss is doing here at Liverpool.
"We won't win the title because Manchester United have become weaker but because we have become better."
Liverpool's financial position has increased speculation about the future of their star names, with Liverpool manager Rafael Benitez consistently denying midfielder Javier Mascherano is on his way out of Anfield.
Torres also believes the Argentinian will stay, adding: "Javier loves it at Liverpool, that is all I can tell you.
"In the summer people like to make a lot of noises about world-class players - and Javier is a world-class player. He has said himself that he is very happy at Anfield and there is no reason for him to want to leave."