The 25-year-old Northern Ireland international, who spent part of last season on loan at League One Coventry, moves to Kenilworth Road on a three-year deal.
Town boss John Still told Luton’s official website: “Josh is a very good player; experienced but a good age, too.
“He’s a busy player, a buzzy one – he can play down the middle as a two or in a three – and he’s versatile, can score and can create goals. I think his all-round play is first-class.
“With Bournemouth’s rise to the Premier League I think he feels as though he’s got to play catch-up with his career again.
“I sense that he’s hungry to resume his career and we’re delighted to have secured his future.”