In the letter President Ahmadinejad offers to "propose new ways" to resolve tensions between the two arch enemies.
The historic move brought an end to a 26-year-old break in official
top-level contacts with Washington, and comes amid US calls for sanctions and even the threatened use of force over Iran's disputed nuclear programme.
However, Secretary of State Condoleezza Rice quashed suggestions of a diplomatic thaw, saying: "This letter is not it."
“There's nothing in here that would suggest that we're on any different course than we were before we got the letter", she added.
Officials said the letter does not address key issues.
"Nothing in the letter addresses the issues between Iran and the
international community," said Frederick Jones, a spokesman for the National Security Council.
Mr Jones said the letter sent on Monday to Mr Bush breaks no new ground on issues of concern to the administration, including Iran's disputed nuclear program and what Washington views as a lamentable human rights record.
"The president was briefed on the letter en route to Florida," Mr Jones said, adding that the White House will not make its contents public.
Mr Jones described the letter as presenting a "broad historical and philosophical exposition" of Iran's past statements defending the country's stance on the nuclear issue.
It is the first time an Iranian president has been known to officially communicate with an American president since Washington and Tehran cut off diplomatic relations in 1980.
"In this letter, while analysing the world situation and finding the roots of the problems, he has proposed new ways for getting out of the existing vulnerable world situation," a spokesman said.
Foreign ministry spokesman Hamid Reza Asefi told the ISNA news agency that "once the American president has received the letter, its content will be made public", while a source in Mr Ahmadinejad's office said the letter has been handed to the Swiss embassy.
Iranian Foreign Minister Manuchehr Mottaki said Tehran would not prejudge the US reaction to the letter.
"We hope that this letter would leave its impact with the same intention, view and expediency that it has been written," he told Iranian TV.
The Swiss government assumed the representation of US interests in Iran in 1981, and has since been acting as a conduit for messages between the two arch-enemies.
The United States and Iran are at loggerheads over Tehran's nuclear programme which Washington suspects is a cover for ambitions to build atomic weapons.
Mr Bush has not ruled out taking military action against the Islamic republic over its nuclear work, and Washington also accuses Iran of supporting "terrorist" groups across the Middle East.
News of the letter came ahead of a meeting in New York of the five permanent members of the UN Security Council plus Germany in a bid to map out a common strategy to force Iran to halt sensitive nuclear fuel work.
And US intelligence chief John Negroponte earlier said the letter could be an attempt to influence the UN Security Council.
He said: "Bearing in mind that I haven't read the letter ... certainly one of the hypotheses you'd have to examine is whether and in what way the timing of the dispatch of that letter is connected with trying in some manner to influence the debate before the Security Council."
The meeting will coincide with continuing bargaining at the Security Council on a Franco-British draft resolution that would legally require Iran to freeze all uranium enrichment and reprocessing activities.
Tehran vowed at the weekend it would refuse to comply with such a resolution, warning the diplomatic crisis was heading toward a "confrontation".
Washington has not had direct diplomatic relations with Iran since April 1980 following the seizure of the US embassy in Tehran in 1979 in which 52 Americans were held for 444 days.
According to diplomatic sources, subsequent communications via the Swiss embassy in Tehran have invariably been between the Iranian foreign ministry and the US State Department - far below the presidential level.
Diplomats from both sides have also held confidential meetings in the past, most recently following the defeat of Afghanistan's Taliban in 2001 and prior to the US-led invasion of Iraq in March 2003.
In an interview published on Sunday (US time), Bush said he preferred a "diplomatic solution" to the nuclear crisis and Iran's threats against Israel, but said that "all options should be placed on the table," including military action.
“When Mr Ahmadinejad says "that he wants to destroy Israel, the world should take that very seriously," Mr Bush said.
Mr Bush has already lumped Iran into an "axis of evil", a view that has only been reinforced by Mr Ahmadinejad's call for Israel to be "wiped off the map" and his view of the Holocaust as a "myth".