A tough, no-nonsense former Marine, with a prosecutorial vocation and a reputation for competence and as a trouble shooter, Mr Robert Mueller III (56) is a Washington insider's choice to head the embattled Federal Bureau of Investigation (FBI).
But Mr Bush's nomination to succeed Mr Louis Freeh, though a conservative Republican, comes to the task with broad bipartisan support and warm recommendations from former colleagues.
The San Francisco US Attorney, a former assistant US attorney-general for criminal prosecutions, faces an uphill challenge in his new role, if, as is likely he wins Senate approval.
Mr Freeh departs two years early from an agency that has been wracked by a series of deeply damaging controversies that have sapped public confidence in the FBI and hit morale within it.
Most recently there was the admission that its agents had failed to pass on to the Timothy McVeigh defence team some 4,500 pages of evidence from regional offices despite repeated demands from head office. An antiquated database system is blamed. And in February the agency had to announce that one of its most senior agents, Mr Robert Hanssen, had, over 25 years, passed to the Russians some of the nation's most closely-guarded secrets.
And then there was the badly mishandled investigation of the Chinese nuclear scientist, Mr Wen Ho Lee - charged with handing secrets to the Chinese, but freed after an agent admitted to lying about him in court.
The agency has an annual budget of $3.4 billion and 30,000 employees, including 11,000 agents, and turning it around will not be easy - middle and senior management is said to have been badly depleted during the Freeh years, a combination of the departure to other jobs of many of the best people and the promotion of what a Clinton aide described as a management culture of "yes men".
In his new man Mr Bush certainly has someone who will not flinch from hard decisions.
One of Mr Mueller's first acts on appointment to the San Francisco Attorney's office was to require all office supervisers to reapply for their jobs. None retained their old jobs and the department saw the beginnings of a rapid turnaround.
And Mr Mueller's commitment to prosecuting murderers as a state attorney - for which he gave up a higher-paid job in the private sector - will endear him to the agency which knows him well. In his previous role in the Justice Department, Mr Mueller oversaw prosecutions of Panama's Gen Manuel Noriega, Mafioso John Gotti, and headed the investigations of the Lockerbie bombing and of the BCCI bank.
Ex-FBI agent Mr Robert Hanssen pleaded guilty yesterday to selling secrets to Moscow and promised a full account of his actions after prosecutors agreed not to seek the death penalty. A court in Alexandria, Virginia was told sentencing was set for January 11th.