Manager Ole Gunnar Solskjaer is trying to rebuild after Cardiff's relegation from the Premier League and has swiftly secured the Austria international on a three-year deal.
Burgstaller scored 12 goals in 35 appearances as Rapid claimed a second-placed finish in the Austrian Bundesliga.
But he could not turn down a move to Cardiff and hopes to endear himself to the club's supporters.
"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 the club's official website.
"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."
The 25-year-old will link up with his new team-mates after Austria's upcoming friendlies against Iceland and the Czech Republic.