A change in designation from Special Prosecutor to Special Counsel was made July 9, 1999. The Rules for the Special Counsel are in 28 CFR 600 under the Authority: 5 U.S.C. 301; 28 U.S.C. 509, 510, 515-519.
The Wikipedia article, Special prosecutor covers this.
Terminating a special counsel investigation:
Generally, the special counsel him or herself decides when an investigation will terminate, with or without formal charges being pursued. The special counsel typically issues a final report on their investigation at this time. The current special counsel regulations specify that[6] "At the conclusion of the Special Counsel's work, he or she shall provide the Attorney General with a confidential report explaining the prosecution or declination decisions reached by the Special Counsel."
28 CFR 600.8:
(c) Closing documentation. At the conclusion of the Special Counsel's work, he or she shall provide the Attorney General with a confidential report explaining the prosecution or declination decisions reached by the Special Counsel.
Once the closing documentation has been provided the investigation is concluded.