The 21-year-old defender joined the Premier League newcomers for £8m on Wednesday, signing a four-year contract.
Caulker, who has one England cap to his name, made 28 appearances in total for Spurs last season but felt he needed to be first-choice at a Premier League club to fulfil his international ambitions.
"If you ask any English player, they have got one eye on the World Cup," he said.
"First and foremost I am going to have to work hard on and off the pitch to earn that sort of achievement, but it is something I am definitely working towards.
"It wasn't that I wanted to leave Tottenham but I am at a stage in my career where I want to play regular football.
"Spurs have three fantastic centre-halves and it may have been a case of being fourth-choice this season and not getting as many games as I would have liked.
"I didn't want to put my career on hold, I wanted to get out and get as much experience as possible and these opportunities don't come around very often.
"I want to help Cardiff progress as a team and progress myself."
Caulker had a loan spell with Swansea City during the 2011-12 season and he says that experience was a factor in his switch to Cardiff.
"I enjoyed my time at Swansea and the people in south Wales are great so it was a no-brainer to move here," he said.
"I thank Swansea for that opportunity, it progressed my career, but now I am a Cardiff player and I hope to go above and beyond for them.
"I spoke to a few Swansea players before their game (against Malmo) last night, I wished them luck and they wished me luck. There are no hard feelings between us as players.
"It will be fantastic to be involved in the derby, I played in a London derby a few years ago and I am definitely looking forward to this one."