The confidential cable written in April 2008 stated Israel, on Sept. 6, 2007, "destroyed the nuclear reactor built by Syria secretly, apparently with North Korea's help," the Hebrew-language newspaper said.
The cable was sent to U.S. diplomats abroad, the report said.
Yedioth Ahronoth said it obtained the cable from WikiLeaks, the whistle-blowing Web site, before WikiLeaks published it.
It is the first official confirmation that Israel was involved in the attack, the newspaper said.
At the time of the airstrike, foreign reports accused Israel of being involved, but Israeli officials refused to comment.
In the cable, Rice related to intelligence compiled prior to the strike on the al-Kibar facility, the newspaper said.
"The American intelligence community engaged in intensive efforts for many months to confirm the information provided to us by Israel about the reactor and collect additional information through our sources and methods," the cable said.
Rice said, "I would like to inform you that the Israeli attack was aimed at destroying the secret reactor built by Syria in a desert area in the east of the country called al-Kibar," the newspaper reported.
The document mentioned Israel's fears that Syrian President Bashar Assad might order an armed response, the report said.
"The Israeli mission was successful – the reactor was destroyed without an option of rehabilitation. Syria completed the site's evacuation, got rid of the evidence of what existed in the area and set up a new building on the site," the cable said.
Yedioth Ahronoth said the cable concluded: "The hiding and lies spread by Syria in the months after the attack are clear proof that it has something to hide. Had it not had something to hide, Syria would not have refrained from inviting IAEA (International Atomic Energy Agency) supervisors and media representatives to the site to prove its claims."