The Hatters are currently fifth in the fourth tier under the 43-year-old, who is in his first managerial job.
"I'm not a fly-by-night. I want to build something here," the Welshman told a Supporters' Trust evening.
"I want to be here long-term. I love the club. I love you the fans."
The former Brighton and Yeovil defender added: "I promise you we will do you proud. I'm not here as a stepping stone. The club is too big for that."
Jones replaced John Still at Kenilworth Road in January 2016, and has won more than half of his games in charge to push Luton towards League One for the first time since 2007-08.
The club recently bought land to build a new stadium at Power Court, and are also moving to a new training ground, which Jones has likened to "going from a tent to the Ritz".
"We have a top Championship environment at the club in terms of how we train and our infrastructure," he said.
"We will achieve what we want to do. We will go to the next level and the one after that. It won't be long until we're a Championship club."
And ahead of Saturday's match against play-off rivals Stevenage, he said his ambitions and those of the club were concurrent.
"I want to be the best manager in the world, and until I get there I won't stop trying. I may never get there, I might not get anywhere near. But until I exhaust every resource then that's what I want to do. It's ambitious, but you have to have ambition.
"With God's will, I've been able to choose a career path and not had to go to certain places I didn't want to, and I've moved because I've wanted to.
"So far I did that here and I picked a wonderful club, and a wonderful club picked me and trusted me and took a gamble on me because a year ago, who knows what could have happened. But it's been a good fit.
"I love the club and I want to take the club forward. I want to move forward myself and look, if I'm here in 20 years' time and we're a Premier League club, that'll be fine by me."
Luton Town boss Nathan Jones has set his sights on becoming "the best manager in the world", but insists he is not using the League Two side as a stepping stone.