Northern Ireland international McCourt has signed a two-year contract and follows former Colchester captain Magnus Okuonghae into the club.
McCourt, 31, was released by Brighton at the end of the season following a loan spell at Notts County.
“What can I say about Paddy? He’s a crowd pleaser,” Hatters boss John Still said on the club’s Twitter account.
McCourt, who has twice won Scottish Premier League title with Celtic, started out in England with Rochdale and has also had spells at Shamrock Rovers, Derry City, Barnsley and Brighton.