Kane signed a five-and-a-half-year deal at Spurs earlier today and it is a signal that the side are looking towards the future.
The 21-year-old has been one of their star performers throughout the campaign so far and Neville and Carragher were both lavish in their praise of the powerful forward.
"They've had [Emmanuel] Adebayor and [Roberto] Soldado, big name strikers and big money strikers, but it's a local boy who's leading the line and he rightly deserves that five-year contract," Carragher said. "They say he's one of their own and that's what it looks he'll be for a long time."
Neville agreed, saying: "I think it's important for Spurs. They needed it. A couple of their signings haven't gone as well as you'd have imagined, particularly the ones that were made a year-and-a-half ago, so I think the fact that they've had someone who has been out on loan many times, they maybe didn't expect him to become the player he has become. But physically he looks a much improved player and his performances this season have been outstanding."
Kane's new deal follows Ryan Mason's last week and it shows that their current squad all want to help the club progress.
Mauricio Pochettino has been keen to develop Spurs' academy graduates and their commitment is sure to be welcomed by Spurs fans.
Kane's future looks particularly exciting, too. The striker has already reached 20 goals this campaign and he looks set to be the main man up-front for many years to come.
There is a feeling that they are currently over reliant on him, though, and Spurs may still be hoping to bring in a striker before the close of the transfer window on Monday.