The deal is the highest transfer fee ever paid for a non-league player - and it is believed that it could rise as high as £1.7 million, depending on conditions.
However the player seems unperturbed.
"I'm not sure a bout the price tag, that's between the chairman here at the chairman at Fleetwood," Vardy told Sky Sports News. "I think every time you play you have a bit of pressure on your shoulders and you have to deal with that.
"As long as I am putting the ball in the back of the net then none of that will matter and everyone will be happy.
"I didn't set a target at all this season. I just wanted to score as many goals as I could and I managed to get to 34. Next season I will do exactly the same, try to get as many goals as I can and hopefully help Leicester get promoted to the Premier League."
Leicester beat off competition from Cardiff to secure the services of the 25-year-old, who scored 34 goals in 40 appearances for Fleetwood last season as they won the Blue Square Premier and earned promotion to League Two.
Leicester first tried to sign Vardy in January, but Fleetwood resisted all approaches with promotion so close.
Sheffield-born striker Vardy is believed to have picked Leicester over Cardiff as they are closer to his family.
Vardy is the Foxes' third signing of the week following the capture of defender Ritchie De Laet and midfielder Matty James from Manchester United.
Defender Matt Mills is expected to leave the club though, with Celtic keen on the player.