The 22-year-old finished his first top-flight season as the highest scorer in the Dutch league by racking up 27 goals to lead AZ to fourth in the table and a place in the Europa League next season.
"We are delighted to announce the signing of Vincent Janssen from AZ Alkmaar, subject to international clearance," the English club said in a statement on its website (www.tottenhamhotspur.com).
Tottenham last month tabled a 14 million euros (£11.8 million) bid for Janssen but the Dutch club demanded 20 million for him.
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Janssen made his international debut earlier this year and has scored three times in five appearances, including one against England in a 2-1 win at Wembley in March.
(Reporting by Mark Gleeson/Ian Rodericks; Editing by Amlan Chakraborty)
