Wheeler was sacked by Town owner Glenn Tamplin recently after just one defeat.
The businessman attempted to get his manager back after admitting to a “big mistake” but his loss is Maidstone’s gain.
The Stones have been under Steve Watt’s caretaker charge since legendary boss Jay Saunders parted company with the Kent club on August 28.
But now it’s Wheeler’s way and chief executive Bill Williams said: “For me this is not taking a chance, it’s giving a chance – much like we did with Jay some seven years ago.
“Terry, Oliver and I spoke at length with Harry yesterday and we were all agreed afterwards that he ticked every box for us.
“He’s got more than 10 years coaching experience, managed more than 250 games and is very much in the mould of the character and personality that we want at the club.
“In Harry we’ve got someone who can lead and take our team forward, while also buying into the academy, community and development programmes we’ve got underway and are looking to expand in the future.”
Watt, who lost all three of his games in charge 1-0, threw his hat into the ring to take them forward.
He wrote in twitter today: “I would like to take this opportunity to say thanks to all the fans for their unbelievable support over the past few weeks, through a difficult period.
“It’s with regret that my time at the club has come to an end again. It was always a wish of mine to return and I can’t thank Jay enough for bringing me back.
“I wish everyone nothing but the best. The fans deserve it.”