Matt has moved to the League Two club for a "significant fee", according to Town chairman Andy Pilley, and will be available to make his debut for The Cod Army against Bristol Rovers on Saturday.
The 22-year-old recently signed a new deal with the Harriers but he was convinced to link up with Fleetwood after holding talks with manager Graham Alexander.
He told Town's official website: "I'm very happy to be here. It was a big draw to be coming to a club in the League, to come up to a club that showed they really wanted me, so I am very happy to be here.
"After I spoke to Graham yesterday (Thursday), it was one of those where his ambition, drive and enthusiasm sold it to me really.
"I think he is similar to me; he is looking to drive on and push onwards and upwards, hopefully I can do the same because that's that kind of thing I am looking do as well, and hopefully we can be a partnership. Hopefully we can move forward."
- Sports & Recreation