Mr Bush has said he believes a full peace deal between Israel and the Palestinians is possible by the time he leaves office in January next year.
Mr Bush's Middle East visit will include Saudi Arabia and Egypt in an attempt to inject some momentum into the current peace talks between the Israelis and Palestinians.
Jerusalem conference
His tour will not take in the Palestinian territories but he will meet Palestinian Authority President Mahmoud Abbas in Egypt.
US president marks 60 years since Israel's foundation
"We believe that the surest way to defeat the enemies of hatred is to advance the cause of hope, the cause of freedom, liberty as the great alternative to tyranny and terror," he said at a peace conference in Jerusalem.
President Bush arrived 60 years to the day after Israel declared independence.
Correspondents describe President Bush's eyes welling with emotion as he received a standing ovation and Israeli Prime Minister Ehud Olmert called him as a "great leader, a great friend".
He and First Lady Laura Bush were met at Ben Gurion International Airport near Tel Aviv by Mr Olmert and Mr Peres.
George Bush and Ehud Olmert address the media
In welcoming Mr Bush, Mr Peres said in its 60 years Israel had "never postponed democracy for a single day nor lost our desire for peace".
President Bush arrived in Israel earlier on Wednesday - 60 years to the day after Israel declared independence.
He added: "You stood like nobody else on our side on sunny mornings and in stormy weather."
But what Israelis celebrate as 60 years of statehood, Palestinians mark as al-Nakba, or "the Catastrophe".
Some 700,000 Palestinians fled their homes or were expelled in 1948.
"We consider the Holy Land a very special place and the Israeli people our close friends," he said.
Many Palestinians also accuse Israel of hurting the innocent and of collective punishment in its attempts to quash Palestinian militants, says the BBC's Katya Adler in Jerusalem.
"I look forward to discussing how I believe our two nations can continue to advance our ideals and approach our next 60 years of partnership with confidence and with hope."
Later on Wednesday, Mr Bush will address a 60th anniversary conference in Jerusalem to be attended by former Soviet leader Mikhail Gorbachev and ex-US Secretary of State Henry Kissinger.
Inauspicious moment
Mr Bush's five-day trip will also include visits to Saudi Arabia and Egypt.
Mr Olmert has been weakened by allegations of corruption
In a BBC interview ahead of his trip, the US president said the current status quo between the Israelis and Palestinians was unacceptable.
He said he would urge the two sides to reach agreement on a future Palestinian state by the end of the year.
"The vision of a [Palestinian] state is such a powerful notion and such an important notion for Israel's very existence, that I do believe that we have a chance to get something defined," Mr Bush told reporters on the eve of the trip.
But BBC diplomatic correspondent Jonathan Marcus says with the Palestinians still politically divided and Mr Olmert weakened by allegations of corruption, this is not an auspicious moment for Mr Bush to be trying to make bold steps in the interests of peace.
As Mr Bush arrived, at least four Palestinians were killed in Israeli military operations in the Gaza Strip, Palestinian doctors said.