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."

The assailants, riding in two vehicles, opened fire on a security convoy on the main ring road in the Nasr City area.
No group has yet said it was behind the attack, which occurred on Monday night.
However, jihadist militants have killed hundreds of police and soldiers since the military overthrew Islamist President Mohammed Morsi in 2013.
Last month, President Abdul Fattah al-Sisi declared a state of emergency after at least 45 people were killed in suicide bomb attacks on two Coptic Christian churches in Tanta and Alexandria.
So-called Islamic State said a local affiliate had carried out the bombings.
Hours before Monday's attack, the UN high commissioner for human rights questioned the measures being taken by Egypt's government to combat jihadism.
Zeid Raad Al Hussein condemned April's church bombings, but told a news conference in Geneva that the "state of emergency, the massive number of detentions, reports of torture and continued arbitrary arrests - all of this we believe facilitates radicalisation in prisons", according to Reuters news agency.
"And abetted by the crackdown on civil society through travel bans, freezing orders, anti-protest laws, this is in our opinion is not the way to fight terror," he added.
"National security yes, must be a priority for every country, but again not at the expense of human rights."
Human rights activists say more than 1,000 people, most of them Morsi supporters, have been killed and tens of thousands arrested in the crackdown.
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.
[NEXT_CONCEPT]
Suspected militants have killed three police officers and wounded five others in an attack in the Egyptian capital, Cairo, the interior ministry says.