Kane's new deal will run until 2022 and extends his stay at White Hart Lane by a further two years.
Spurs had never considered selling their talisman but uncertainty over negotiations had led to unwelcome speculation about his future.
Kane, however, remains committed to the club he first joined as an 11-year-old and Pochettino believes he could stay at Tottenham for the rest of his career.
"He could be like this type of player for us," Pochettino said.
"He is English and one of the best strikers in the world and teams, not only in England but in Europe, have seen him and been following him and thinking there would be a possibility one day to take Harry.
"But Harry is very happy here and one more time has shown his commitment to the club and that is fantastic."