He joins other performers including Gil Scott-Heron and Santana, who have dropped tours in Israel in recent months.
His decision contrasts with those of Paul McCartney in 2008 and Leonard Cohen last year, both of whom played dates in Israel.
Costello said he had hoped that music was more than "mere noise, filling up idle time."
But added: "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 ..."
Costello said the coming gigs would have been attended by many people who question Israeli policies "on settlement and deplore conditions that visit intimidation, humiliation or much worse on Palestinian civilians in the name of national security."
But at the same time he said he was equally aware of the sensitivities behind those themes and "of so many despicable acts of violence perpetrated in the name of liberation."
He said that in the end his conscience and instinct told him that if these themes were "too grave and complex" to be addressed in concert, "then it is also quite impossible to look the other way."
He apologised to fans, and many in the Israeli media who he said had helped him to gain an understanding of the cultural scene.
Costello said he regretted the fact that he probably would not receive another invitation to play in Israel, but imagined "a better time" when he would not be penning such a statement.
"Sometimes a silence in music is better than adding to the static and so an end to it," he said.
(Reporting by Stefano Ambrogi; Editing by Myra MacDonald)
COPYRIGHT: (c) Reuters 2010. All rights reserved. Republication or redistribution of Reuters content, including by caching, framing or similar means, is expressly prohibited without the prior written consent of Reuters. Reuters and the Reuters sphere logo are registered trademarks and trademarks of the Reuters group of companies around the world.