The defender has agreed a three-year contract with the Premier League newcomers, who will play Chelsea on their return to the top flight on Monday.
The 28-year-old told the club's website: "I'm absolutely thrilled. I've had eight years at Wolves now and I was on loan at Brighton last year but to start a new chapter in my career is great.
"I don't think I could have picked a better place than Turf Moor and, obviously, to come to the Premier League is a massive pull as well.
"Once you get a taste of it, you want to play as much Premier League football as you can. Burnley have done superbly well to get promoted and hopefully I can play some part in us having a successful year."
Ward has 24 caps for the Republic of Ireland.