Kalajdzic, who has 15 caps for Austria, joins Wolves on a five-year-deal, with the option to extend for a further 12 months.
Wolves did not mention the transfer fee but British media reported they paid 18 million euros plus add-ons for the striker, who will compete with forward Raul Jimenez (31).
"I'm two metres tall, but also not bad with my feet. I'm just hungry to score goals," said Kalajdzic, who was Stuttgart's leading scorer in the last two Bundesliga seasons with a total of 23 strikes.
"Everyone tells me the Premier League is the toughest league, it's the NBA of football. I'm just excited to prove myself against the best because in this league the best players are playing."
The transfer window for the Premier League will close at 23:00 CET on Thursday.
Wolves are second from bottom in the standings after four matches.
They are due to travel to Bournemouth later on Wednesday.
