The England international was a target for Arsene Wenger last year, with the Gunners reportedly happy to activate his £20million release clause, but he chose to stay with the Premier League champions.
Vardy only scored five times in his first 22 league games this season but has recaptured something like his top form since the departure of former boss Claudio Ranieri, having hit six in his last seven appearances in the top flight.
Although Shakespeare feels Vardy has yet to get back to his very best, he feels that he has justified his decision not to move to north London.
"Thankfully, he chose us," said Shakespeare ahead of Leicester's trip to Emirates Stadium on Wednesday. "All players will go through peaks and troughs, they just have to stay mentally tough, which Jamie did.
"Players can't think: 'If I have one bad game, maybe I made the wrong decision'. It's about rolling your sleeves up and making sure you turn those indifferent performances into good performances.
"The Jamie we're seeing out there at the moment is full of confidence and a goal threat as well. He's banging in the goals and we need that to continue to the end of the season.
"I am reluctant to say he is back to his best, as I want more from him, but his goalscoring of late has been very good.
"Strikers go through purple patches. Then there are the dark times when whatever they hit doesn't go in.
"At the moment, you see a player full of confidence and full of running. We need that to continue because we need a Jamie Vardy threatening defenders, getting on their shoulders and being a goal threat as well."