The Congressional Research Service explains the appointment process for circuit court nominees, after Senate confirmation, as follows [Link]:
After Confirmation of a Nomination Reconsideration
Senate Rule XXXI provides that, after the Senate has confirmed a nomination, any Senator who voted with the majority has the option of moving to reconsider the vote. Only one motion to reconsider is in order on the nomination, and it must be made on the day of the vote or on one of the next two days the Senate meets in executive session. Typically, however, the Senate, before the vote on confirmation has occurred, preempts the motion to reconsider, arranging beforehand by unanimous consent for it to be considered tabled in the event the nomination is confirmed. It is typical, for example, for the Senate, in a unanimous consent time agreement for a confirmation vote on a circuit or district court nomination, to include the provision that, after the vote, “the motion to reconsider be considered made and laid upon the table.” Similarly, UC agreements concerning upcoming cloture votes on nominations often provide for the tabling of the motion to reconsider in the event cloture is invoked and the nominee then confirmed. In either case, tabling the motion prevents any subsequent attempt to reconsider.152
Resolution of Confirmation
With the motion to reconsider tabled, the Secretary of the Senate attests to a resolution of confirmation and transmits it to the White House. (In the rare instance of the Senate voting against confirmation, the Secretary will transmit to the President a resolution of disapproval.) Senate Rule XXXI requires that the Secretary wait until the time for moving to reconsider has expired before notifying the President that a nomination has been confirmed. Such notice, however, in practice “is usually sent immediately, permitted by unanimous consent.”153
Post-Senate Appointment Steps President Signs Commission154
Upon notification of a nominee’s confirmation, the President performs the next step in the appointment process—the signing of the nominee’s commission. The commission is a formal document empowering the nominee to assume the judicial office, which the President must sign before the nominee may begin his or her new duties. The date of a nominee’s commission is the date the President signs it, which usually occurs within a few days of Senate confirmation (but can also occur on the same date as the confirmation itself). The commission is transmitted to the Department of Justice, which then sends it, as well as a packet of other documents, to the nominee.
Oath of Office
The appointment commission packet sent by the Department of Justice includes various forms to accompany the statutory oath of office, which each circuit and district judge must take before exercising the judicial authority of the United States. The oath of office is orally administered by someone legally authorized by state or federal law to administer oaths, including the chief judge or another judge on the court to which the nominee is assuming his or her position. Additionally, in some cases, the home state Senator of a nominee has administered the oath of office. The oath is a combination of the judicial oath of office required of every Justice and judge of the United States under 28 U.S.C. 453 and the general oath administered to all federal government officials, set forth in 5 U.S.C. 3331.155
At the time the oath of office is executed, the nominee himself or herself must also sign and date the commission. If two or more confirmed nominees to the same court sign their commissions on the same date, seniority is determined by seniority of age of the nominees. If, for example, Judges A and B both sign on the same date and Judge A is older than Judge B, then Judge A is considered more senior than Judge B.156
This process—receipt of the packet from the Department of Justice, administering the oath of office to the nominee, including obtaining his or her signature on the commission—typically occurs within a week or two of Senate confirmation. In some cases, however, a nominee might wait longer, for professional reasons, to take the oath and sign his or her commission. For example, a law professor who is confirmed as a U.S. district court judge might wait to sign her commission until after she has finished teaching for the semester.
Typically, the last step in the appointment process is the investiture. At this ceremonial event, attended by family and friends, the new judge is sworn in yet again, in the courtroom. The ceremony, however, is not required for the nominee to assume office and can take place weeks or months after the oath of office is executed.