The Leicester striker was a top target for Gunners manager Arsene Wenger during the transfer window and weighed up a move to the Emirates prior to England's Euro 2016 campaign.
However, the 29-year-old instead signed a new contract with the Premier League champions, to the delight of BT Sport presenter and former Foxes favourite Lineker.
"It was a big moment, and it was a very surprising moment," said Lineker
"I thought it said a lot about him as well.
"It's not all about the big pay day and stuff - especially at this time in his career as it was perhaps his one and only chance of moving to a bigger club. It was a really significant moment.
"It spoke a lot about him and the club and the fact there are ambitions at Leicester."
Some felt Vardy's game time would be limited had he moved to north London, but Lineker added: " I think he'd walk into Arsenal's team. Have you seen their centre-forwards?
"They're fine but they're not as prolific as Vardy. They are not as quick as Vardy and they don't give you the options Vardy does. Olivier Giroud is a certain kind of target man. He will get his one goal in three or whatever it is.
"Lucas Perez, who they've brought in, I quite like but he's not going to be as prolific as Vardy. All players believe they will start anyway if they've got anything about them. You can tell Vardy is full of confidence."
Source: PA