Money, who spent one year at Kenilworth Road as a player, has left his role at Newcastle as club's academy director to take up the role.
Alan Neilson, who has been acting as caretaker manager since the departure of Harford, will work as Money's assistant.
The former Walsall boss has set his sights on guiding Luton back to the Football League at the first time of asking.
"I've seen the squad here and there is a huge amount of ability - there's no question about that," he said.
"They have been very unlucky with injuries to be fair, but you have to deal with that. The players create a lot of chances and they are solid at the back. The fans can help and build their confidence - be that 12 man.
"There's no doubt this team is capable of finishing top at the end of the season. That's my focus."