"The Director of the Federal Bureau of Investigation (FBI) is appointed by the President by and with the advice and consent of the Senate. The statutory basis for the present nomination and confirmation process was developed in 1968 and 1976, and has been used since the death of J. Edgar Hoover in 1972. Over this time, seven nominations have been confirmed and two have been withdrawn by the President before confirmation. The position of FBI Director has a fixed 10-year term, and the officeholder cannot be reappointed, unless Congress acts to allow a second appointment of the incumbent. There are no statutory conditions on the President's authority to remove the FBI Director. Since 1972, two Directors have been removed by the President. President William J. Clinton removed William S. Sessions from office on July 19, 1993, and President Donald J. Trump removed James B. Comey from office on May 9, 2017. Robert S. Mueller III was the first FBI Director to be appointed to a second term, and this was done under special statutory arrangements. He was first confirmed by the Senate on August 2, 2001, with a term of office that expired in September 2011. In May 2011, President Barack Obama announced his intention to seek legislation that would extend Mueller's term of office for two years. Legislation that would allow Mueller to be nominated to an additional, two-year term was considered and passed in the Senate and the House, and President Obama signed the bill into law (P.L. 112-24) on July 26, 2011. Mueller subsequently was nominated and confirmed to the two-year term, and he served until September 4, 2013."
CRS Report for Congress, R44842
Federation of American Scientists: http://www.fas.org/sgp/crs/index.html