The 22-year-old lit up the Eredivisie last season and bagged 27 goals en route to the Golden Boot award and will now look to play a starring role under Mauricio Pochettino at Spurs.
"We are delighted to announce the signing of Vincent Janssen from AZ Alkmaar, subject to international clearance," the club confirmed on Tuesday.
"The striker has signed a contract with the club until 2020."
The player also revealed his delight at having secured a move to the English Premier League.
"I'm incredibly happy that I can make this step to Tottenham Hotspur," he told AZ's official website.
"I'm glad the clubs finally agreed. I've shaken everyone's hand and I leave via the front door. I think it's a great deal for all three parties.
"I'm leaving for a great football nation and will play in the Champions League. I had the best footballing year of my life with AZ.
"The people I've worked with were fantastic. I can only look back on my time in Alkmaar with a positive feeling."