Steve McClaren has splashed out €8million to land the highly-rated frontman, who had been interesting Aston Villa.
The 24-year-old, who joins from Dinamo Zagreb, is delighted to have completed the move and is relishing the prospect of a fresh challenge in Germany.
"My wish was to play in the Bundesliga," said Mandzukic.
"Now I'm at a very good club and I hope that I will justify expectations."
Mandzukic becomes McClaren's third signing since taking the reins at Wolfsburg this summer, with Arne Friedrich and Simon Kjaer having already been snapped up.
The club are looking to piece together a squad capable of reclaiming the Bundesliga crown they relinquished to Bayern Munich last season.