De Zerbi, 46, arrived on Wednesday at Hotspur Way, and sent a video message to Spurs fans via the club's social media channels.
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“Hello all the Tottenham fans,” the Italian said.
“I am very happy to stay here with you. It is a very big honour and I am very proud to be your coach. I want to give my best. I want to stay for a long time in this big club. See you soon.”
De Zerbi’s first game in charge is at Sunderland on April 12.
Tottenham currently sit one point above the Premier League dropzone.