The 27-year-old joins the English Championship club for an undisclosed fee after 18 months in Edinburgh.
Chief executive Ben Kensell both paid tribute to the former Hibee and heralded the importance on the sale in a statement on the club website.
He said: “We’d like to thank Matt for his contribution and efforts during his time at the club.
"On and off the pitch, Matt was a model professional and we wish him all the best for the future.
"To grow Hibernian FC and to provide further transfer funds for our squad, player trading is vital, alongside increasing our club-controlled income.
"I’d like to thank Luton for the way negotiations were conducted and we believe we’ve got a really beneficial deal for our football club.”
The 6ft 7in stopper signed from Arsenal in the 2021 January transfer window. He initially played understudy to Ofir Marciano – though did feature in all of the club’s Scottish Cup matches as Hibs made it to the final – before becoming No.1 this past season.
The arrival of David Marshall in the summer put Macey’s position in doubt with back-ups Kevin Dabrowski and David Mitchell all signed up through to the end of next season, which was when Macey’s old deal was set to expire.
In total he played 52 games for Hibs, including five matches at Hampden Park as Hibs made it to at least the semi-finals of both the League Cup and Scottish Cup during his time.