The two leaders are expected to focus on terrorism, trade, investment and collaboration on technology.
However, there are no signs that Washington is prepared to support a campaign to include India in a reformed United Nations Security Council.
During the talks India is hoping to strike a deal on ways to share nuclear technology, which correspondents say Washington has been reluctant to agree because of India’s refusal to join international nuclear non-proliferation treaties.
But there are indications that Mr Bush will invite India to join in some international nuclear research projects.
Indian newspapers are calling Mr Singh’s visit “historic” – and “waiting for some history to be made”.