Bush, seen as the most pro-Israel US president ever and a supporter of Prime Minister Ariel Sharon's unilateral Gaza pullout plan, was expected to nominate Rice on Tuesday to replace Colin Powell, who announced his resignation on Monday.
"For us it does not make much of a change," a senior Israeli official said about Rice's appointment.
"We have a friend in the White House, and this is important. The strategic ties between Israel and the United States have never been stronger."
It is conventional wisdom in Israel that Powell was, in the words of commentator Nathan Guttman in the Haaretz daily, "a figurehead, not a player" and that Middle East moves were directed by Bush and Rice, seen as friendlier toward the Jewish state.
As national security adviser in Bush's administration, Rice has spearheaded US dealings with Sharon since he became prime minister in 2001, holding frequent meetings with his chief adviser, Dov Weisglass.
Rice has been a vocal advocate of a policy that adopted Sharon's refusal to deal with the late Palestinian president, Yasir Arafat, and demanded a new Palestinian leadership "not compromised by terror".
"She's a very sharp player," one Israeli official said. "When she wants to be firm, she can be firm. When she wants to be tough, she can be tough."
Rice is considered to be more
pro-Israel than Powell
With the Middle East landscape changed by the death of Arafat, Nabil Abu Rudaina, a senior aide to the late leader and now adviser to caretaker President Rawhi Fattuh, urged Rice to speed up implementation of the road map.
"We hope the American administration will resume its direct contacts with the Palestinian Authority and not waste time," Abu Rudaina said.
A US official said Powell will visit Ramallah, the West Bank seat of the Palestinian Authority, and meet Israeli leaders in Jerusalem this month.
It will be his first such trip since 2003 and follows US pledges to help the Palestinians prepare for a presidential election on 9 January.
'The strategic ties between Israel and the United States have never been stronger'
Senior Israeli official
Looking ahead to Rice's stewardship in the State Department, Palestinian cabinet minister Saib Uraiqat called her "a very dignified person, with an analytical mind".
"I think we will be working closely with her in the hope of implementing President Bush's vision of a two-state solution in his second term," Uraiqat said.
Middle East writer-analyst Samir Atalla warned of "a tougher stance by Washington on all issues" because Bush's administration is losing the voice of Powell, who often was more moderate than other officials, particularly Vice President Dick Cheney.
He said that one area where the US position may not harden is the Palestinian issue because Bush has made "a clear commitment ... to a Palestinian state," he said on the LBC news channel.
Uraiqat described Rice as a
Rice is a long-time trusted adviser of both Bush and his father, the former president. She worked at the National Security Council in the first Bush administration.
Before becoming Bush's national security adviser in January 2001, Rice spent six years as provost at Stanford University, the institution's chief budget and academic officer.
She is an expert on Soviet and East European foreign and defence policy.
Ever since Bush walked into the Oval Office, Rice has been busy keeping Powell and Defence Secretary Donald H. Rumsfeld from butting heads; orchestrating a North Asia policy designed to get North Korea to let go of its nuclear ambitions; helping the president deal with Iran's nuclear weapons programme; and shepherding work on the Middle East peace process.