Money suffered a heart attack a couple of months ago but has succeeded Mick Harford as the manager of the Conference side.
He had been at Newcastle running their Academy and for a while helping Chris Hughton with the first team after leaving Walsall in April 2008.
Speaking to Luton's club website, Money said: "I've seen the squad here and there is a huge amount of ability. "There's no doubt this team is capable of finishing top at the end of the season. That's my focus.
"I'm sure there will be changes to what people are used to, but no two managers are alike so you have to adapt to achieve success.
"Everything is in place to move forward and to move forward from a play-off place is a great place to start."