The Tottenham Hotspur man penned a contract extension on Thursday.
The 23-year-old striker will reportedly earn over £100,000 a week on his new deal, according to BBC Sport.
It is a big weight off the mind for Tottenham following reports last month that he was reluctant to sign a new contract.
The English striker's value to Spurs cannot be understated by virtue of the fact that he has netted over 70 goals for the Lilywhites since breaking into the side two years ago.
And King, a one-club man at Tottenham himself until 2012, believes Kane could end up retiring at White Hart Lane.
"He could be a one-club man," King told ESPN. "The club are progressing, going in the right direction and, while they're doing that, Harry will be happy, but you can never talk for someone else.
"I was someone who loved playing here, I had great relationship with the fans and that was important to me.
"I'm sure Harry feels the same way. If the club are playing at the highest level, trying to win trophies and the league, there is nowhere else to go."
Kane will be hoping to mark the celebratory event by finding the net on Saturday against Swansea - Tottenham need him to.
Mauricio Pochettino's side are already seven points behind top-of-the-table Chelsea - who beat them at Stamford Bridge last weekend - and losing at home to Swansea could be detrimental for their Premier League title hopes.