The 25-year-old has put pen to paper on a three-year deal with the Bluebirds, who were relegated to the Championship after finishing at the bottom of the Premier League table last season.
"My decision to join Cardiff City was never in question when the club first contacted me, it has always been a dream for me to play in this country," Burgstaller told Cardiff City Player.
"I've followed Cardiff in the Premier League last season and I'm very proud and honoured to be given the chance to wear the Cardiff City jersey. I'm a big admirer of the passion of the fans here."
Burgstaller joins Ole Gunnar Solskjaer's side after scoring 12 goals in 35 appearances in the Austrian Bundesliga during the 2013-14 campaign.