Now the president's brain really is missing ...

A White House spokeswoman acknowledged that Mr Rove would be nigh-on irreplaceable, saying his departure is "a big loss for us".

Mr Rove, 56, told the Wall Street Journal that he felt it was time to retire to "the Texas hill country".

"There's always something that can keep you here [Washington] and as much as I'd like to be here, I've got to do this for the sake of my family," said Mr Rove. "I just think it's time."

The White House chief of staff, Josh Bolten, had asked staff to leave their posts now or commit to serving the president until his term in office ends in January 2009.

The president bade Mr Rove an emotional farewell. "Karl Rove is moving on down the road," Mr Bush said, appearing grim-faced outside the White House with Mr Rove at his side.

"We've been friends for a long time and we're still going to be friends ... I'll be on the road behind you here in a bit," he added ruefully.

Mr Rove, his voice quivering at times, said: "I'm grateful to have been a witness to history. It has been the joy and the honour of a lifetime. But now is the time."

After a lengthy hug from Mr Bush and then his wife, Laura, Mr Rove joined them on the president's helicopter.

Mr Rove's resignation ends a remarkable political partnership that, beginning in 1993, carried Mr Bush to two terms as a popular governor of Texas and then to two - more controversial - terms in the White House.

Through it all, Mr Rove was known as "the architect" of a string of Republican victories that increased their grip on power in Washington - at least until last year's disastrous mid-term elections, when Congress swung back to the Democratic party.

More pejoratively, opponents and TV chat-show hosts often referred to Mr Rove as "Bush's Brain". The president himself bestowed the moniker of "Turd Blossom" upon his erstwhile right-hand man - a nickname derived from a Texas flower that is happiest in cow dung.

Mr Rove's departure means Mr Bush has lost all but a handful of the loyalists who entered the White House with him in January 2001.

Vice-president Dick Cheney is the only Bush confidante to remain in the same job. Condoleezza Rice has moved out of the White House to serve as secretary of state while former White House counsel Alberto Gonzales now runs the sprawling justice department as attorney-general.

Since the Democrats won control of Congress in November, some other Bush officials have announced their resignations. Among aides who have left are Dan Bartlett and Harriet Miers.

The defence secretary Donald Rumsfeld was forced out immediately after the last election as the war in Iraq dragged on, Colin Powell stepped down as secretary of state in 2005, and the attorney-general John Ashcroft went in 2004.

Mr Bush stood by Mr Rove amid calls that he should be sacked for his part in the leaking of a CIA officer's identity as part of a White House plan to discredit opponents of the Iraq war. Mr Rove made no fewer than five appearances before a grand jury investigating the Valerie Plame affair.

But Mr Rove was adamant yesterday that he was not leaving to avoid close scrutiny from congressional Democrats investigating the White House's role in the controversial sacking of a number of US legal figures, supposedly for partisan political reasons. "I'm not going to stay or leave based on whether it pleases the mob," Mr Rove said.

Mr Rove's reputation - already high - was burnished still further when Republicans won sweeping gains in the 2002 mid-term elections; in 2004 Mr Bush increased his vote total by 25 per cent on his 2000 win - a testament to the electoral machine Mr Rove designed.

Republicans made further gains in both the House of Representatives and the Senate that year - the first time that had happened to a sitting president since 1936, Mr Rove said.

Not content with a strategic role during Mr Bush's second term, Mr Rove was appointed deputy White House chief of staff, with a special responsibility for policy development.

However, a series of miscalculations and political defeats in Congress have tarnished Mr Rove's reputation. His determination to "think big" and press for the privatisation of social security backfired; while the increasingly rancorous tone of the debate on the Iraq war disillusioned many of the centrist voters Mr Bush had won in 2000.

Last year, Democrats also regained control of both the House and the Senate.

'Boy genius' with a troubled past who masterminded key victories

THE "Boy Genius" - as Karl Rove was not unhappy to be known - enjoyed a remarkable run of political success until Democrats regained control of Congress last November.

For 30 years Rove specialised in running aggressive campaigns that took no prisoners and his string of victories endowed him with an aura of omnipotence he was prepared to tolerate, even if he did sometimes blanch at stories celebrating or condemning "The Mark of Rove".

Mr Rove dropped out of the University of Utah in 1971 to work for the College Republicans and earned his first political stripes two years later when, after a dirty, controversial campaign, he became chairman of that group - a key position that has traditionally been a staging post on the road to higher, better things in the conservative movement.

Mr Rove moved to Texas and in 1978 helped Bill Clements become the first Republican in 100 years to become governor of the Lone Star State.

Mr Clements lost four years later, in 1982, but won again in 1986 and a campaign memo from that election shows the quintessential Rove style: "The whole art of war consists in a well-reasoned and extremely circumspect defensive, followed by rapid and audacious attack." And: "Anti-White [Mr Clements' opponent] messages are more important than positive Clements messages. Attack. Attack. Attack."

Mr Rove learnt his political skills from Lee Atwater, a legendary tough, hard-nosed and cynical Republican operator who was, inter alia, credited with destroying the Michael Dukakis presidential campaign in 1988. By the mid-1990s Republican candidates across the country were hiring Mr Rove's consulting firm.

Among them was George W Bush, for whom Mr Rove orchestrated a successful campaign to become governor of Texas in 1994. The men had first met in November 1973. George Bush snr asked Mr Rove to take a set of car keys to his son, George jnr, who was visiting home during a break from Harvard Business School. It was the first time the two met. "Huge amounts of charisma, swagger, cowboy boots, flight jacket, wonderful smile, just charisma - you know, wow," Mr Rove recalled.

In Texas, Mr Rove encouraged Mr Bush to reach across the aisle, bringing Democrats into the fold. In 1998 Mr Bush was re-elected by a landslide.

Mr Rove determined that Mr Bush must run for the presidency in 2000 as a "compassionate conservative" - pitching himself as a Republican who understood the hopes and fears of ordinary working and middle class Americans.

After the terrorist attacks of 11 September, 2001, Mr Rove used national security and the war as a wedge issue to split the Democratic party. Mr Bush had run to the centre in 2000; now he would run to the right and win elections on turnout and organisation, not by winning swing voters.

He was rewarded with Congressional gains in 2002 and re-election in 2004, but Mr Rove's hopes for a permanent political realignment were dashed by Republican profligacy in office and the unpopularity of the war.

In Washington, Mr Rove helped ensure that the era of paying lip-service to the ideal of "small government" was over. The tax cuts he pushed for in the first term may have proved popular with conservatives; massive increases in government spending were not. Federal spending on education and health soared, repudiating Reaganite orthodoxy and traditional Republican rhetoric.

Karl Rove's childhood in Colorado and Utah was not always easy. At high school he was a self-confessed nerd and political junkie. His father walked out on his mother in on Christmas Day 1969 - his 19th birthday. Years later, Mr Rove discovered that the man he believed to be his father was not, in fact, his biological father. In 1981, Mr Rove's mother committed suicide.

Mr Rove avoided the possibility of being drafted to serve in Vietnam by receiving a college deferment.

Mr Rove has been married twice and has one son who begins college in Texas this autumn.

He is now expected to write a book.