Shaw, who joined the Mariners from Gateshead in the summer of 2016, has won five trophies and two promotions during his three years at the club.
The defender - who has made 142 appearances for Shields, and scored 21 goals - is now eager for more success after putting pen to paper.
He said: "I never wanted to leave and everyone knows that.
"It has never even been a conversation.
"We had a disappointing end to last season but as I said at the time, my focus straightaway shifted to next season.
"To get myself sorted and tied down is all I ever wanted.
"I'm sure fans will see that some people have left the club, but the positive thing is that a lot of players have re-signed so a massive chunk of that successful squad from the last couple of seasons are still here.
"We trust the club to bring in good players around us, but the focus is exactly the same.
"We're in it to win it."
The Shields squad are expected to return for pre-season in around a month's time, something Shaw is already eagerly anticipating.
He added: "Nobody wants the season to finish when you're on a good run but sometimes when it ends as last season did, you need that break.
"You need to just shut down, walk away from the game, spend time with your family and friends and almost ignore that football exists.
"That lasts for two or three weeks.
"In a month's time we're going to be at it again and we just can't wait now."
South Shields joint manager Lee Picton said: "It goes without saying that we're absolutely delighted to retain the services of Jon.
"Jon brings incredible leadership both on and off the pitch and from day one of being at the club, he has set the highest possible standards for other players to follow.
"Every successful club has personalities like Jon and the more personalities we have like him in the dressing room, the better we will be as a football club."