Mueller was former FBI director James Comey's predecessor. President Donald Trump fired Comey last week.
The longtime litigator was the second-longest FBI director in history, only behind iconic and controversial director J. Edgar Hoover. Congress passed legislation in 2011 to extend Mueller's term from the usual 10 years, giving him a 12-year tenure.
Mueller, 72, oversaw the FBI from September 4, 2001, just days before the September 11, 2001, terrorist attacks, until September 4, 2013.
Mueller is widely seen as a nonpolitical, dogged investigator, respected on both sides of the aisle. The extension of his term passed the Senate 100-0, and he was also initially confirmed in 2001 unanimously, 98-0.
Since leaving the FBI, Mueller has not been a stranger to high-profile investigations.
In 2015, Mueller conducted an inquiry
into the NFL's handling of a video of former running back Ray Rice punching his then-fiancée. And last year, Mueller was asked
by Booz Allen Hamilton to conduct a security review after a contractor was arrested for allegedly stealing national security secrets.
Philip Mudd, a CNN contributor and former deputy director of the FBI's national security branch under Mueller, praised the appointment to CNN's Wolf Blitzer on Thursday.
"Every American who thinks that this is a moment of turmoil, whether they like the President or not, should breathe easy tonight: Robert Muller is solid ground," Mudd said.
"He is not one of the best, Robert Mueller, he is the best I ever saw. Leadership, judgment, decision-making," he added. "There is nobody better at doggedly pursuing a target without being subjected to any pressures from Congress, the President, the media, anybody in the FBI, the attorney general, the deputy attorney general. There is nobody better."
Atop the FBI, Mueller saw the bureau through a time of tremendous change in a post-9/11 world. His tenure saw the rise of al Qaeda as a threat, the vast expansion of US surveillance capabilities and an increase in the threat from home-grown terrorism. Mueller reflected on the changes in an exit interview
with CNN in 2013, saying the intelligence collection capabilities the US built since 9/11 could possibly have stopped part of the attacks.
Mueller also was part of another famous incident with Comey -- a dramatic 2004 dispute over the Bush administration's warrantless wiretapping program.
Comey was serving as acting attorney general as then-Attorney General John Ashcroft was hospitalized. Comey refused to reauthorize the controversial Bush administration program over concerns about the legality of the surveillance.
The White House counsel and chief of staff rushed to the hospital to attempt to get Ashcroft to sign the reauthorization -- and Comey rushed to stop them, though the program was eventually reauthorized without Justice Department approval. Mueller's notes backed up Comey's account when the incident was revealed three years later, and Mueller joined Comey in threatening to resign in 2004 if the program was not overhauled.
Mueller's FBI stint capped a long career working in law, including breaking ground.
After decorated service in the Marine Corps in Vietnam, Mueller graduated from University of Virginia Law School, according to his FBI biography
He worked for 12 years in the US attorney's offices, serving for some time as chief of the criminal division in the Northern District of California in San Francisco, and also working as an assistant US attorney in Boston.
He worked for a time in the private sector before moving back into government as an assistant to the attorney general in 1989, moving quickly to run the department's criminal division.
As chief of the criminal division, Mueller saw the creation of the agency's first cyber-dedicated unit, putting himself on the leading edge of a field of crime fighting and national security that has only grown more important.
Prior to joining the FBI in 2001, after he left Justice Department headquarters, Mueller served as the US attorney in San Francisco.
After leaving the FBI, Mueller joined private law firm WilmerHale, from which he is resigning to take the special counsel role.
Mueller is married and has two daughters.