Costello, one of the most gifted British songwriters of his generation, was due to play on 30 June and 1 July but says his "conscience" dictated that he pull out of the performances.
He joins a list of performers who have decided not to play in Israel, including Gil Scott-Heron and Santana.
On his website, Costello wrote: "Then there are occasions when merely having your name added to a concert schedule may be interpreted as a political act that resonates more than anything that might be sung and it may be assumed that one has no mind for the suffering of the innocent.
"I must believe that the audience for the coming concerts would have contained many people who question the policies of their government on settlement and deplore conditions that visit intimidation, humiliation or much worse on Palestinian civilians in the name of national security.
"I am also keenly aware of the sensitivity of these themes in the wake of so many despicable acts of violence perpetrated in the name of liberation.
"It is a matter of instinct and conscience.
"I cannot imagine receiving another invitation to perform in Israel, which is a matter of regret, but I can imagine a better time when I would not be writing this.
"With the hope for peace and understanding. Elvis Costello."Source: The Guardian