New Foxes boss Claudio Ranieri had held talks with the 34-year-old, urging him to make his mind up as the club needed to know if he was staying on after his deal expired last month.
In a statement on his Facebook page, the player said: " I would like to announce that I have decided not to renew my contract with Leicester City
"I have taken this decision only 24 hours after receiving the proposal from Leicester because I want to give the club as much time as possible to find an alternative."
Cambiasso's decision will come as a blow to Ranieri, who said on Monday - at his first press conference since replacing the axed Nigel Pearson - that keeping the former Argentina international was a priority
''I've had a conversation with him
I have spoken to him, I know him from Inter Milan, I coached him there
I said to him 'I need you, everybody loves you in Leicester, please come back','' the Italian had said
''He told me he wants to wait and look at all the opportunities offered to him and then he will choose
But we need 'Yes or no' because at the start of the season he is a team leader and if he doesn't come I need another team leader
We don't start the season without a player like him.''
Cambiasso proved a key figure last season as Leicester won seven and drew one of their final 10 games to retain their Barclays Premier League status
The player's statement continued: "I would like to thank all the fans who last season made me feel proud to be part of a club with an unforgettable spirit and energy
"And a very special thanks to all my team-mates, staff and every people of the club, with whom I have lived one of the most important years of my career, crowned with the remaining EPL status.
"Many thanks to everyone, keeping you all forever in my heart
Leicester City Football Club."
Source : PA
Source: PA