Chong completed a permanent transfer to Birmingham from the Red Devils last summer after a couple of loan spells at the club.
The 23-year-old made 38 appearances and scored four goals as Birmingham finished 17th in the Championship.
Chong now has the chance to make his mark in the Premier League after making just five appearances in the top flight when he was a Manchester United player.
Speaking after being unveiled as the club’s third signing of the summer, for a fee believed to be around £4m, Chong told Luton's website: “In the few hours that I’ve been here I already get the feeling that it really is a family club.
“I’m a football fan, I've watched some games so I’ve seen how they [the team] have played and it shows togetherness and unity – and you can only have that if you’re a family club. I think that’s important because every club faces adversity – it’s not always going to be good – but if you’re a family club you stick through it together and it’s easier as a family.”
Luton boss Robb Edwards added: "Tahith is someone that I, and the club, have known for a very long time."
"I first crossed paths with him when I was at Wolves a few years ago and he was in Manchester United's Under-23s.
"I've liked him from then, and he was a bit more of a winger at the time. Looking at him in a lot more detail at Birmingham this year, he's been able to play inside as a midfield player as well."
Luton will start their first Premier League campaign away at Brighton on August 12.
