The France international signed a five-year deal last week, and the Spurs boss is delighted to see his goalkeeper extend his stay at White Hart Lane.
He told the club's official website: "This is very good news for Tottenham, for us and his teammates.
"Hugo is a great goalkeeper and it's very important he's excited to stay with us. We are excited that he's going to be here with us. It's very important for the future."
Spurs fly out for their tour of the United States on Wednesday.