The stalking emerged during its investigation into an email scandal that led to the highly decorated general's resignation.
Gen Petraeus resigned in November after acknowledging the extramarital affair, which was exposed after Ms Broadwell emailed Florida socialite Jill Kelley, allegedly warning her to stay away from General Petraeus and Gen John Allen, the US commander in Afghanistan.
Ms Kelley reported the emails to the FBI, triggering an investigation that also led the FBI to Kelley's emails to the married Allen, who is now under investigation by the Pentagon's inspector general.
A spokesman for Ms Broadwell said she and her family are "pleased with this decision and pleased that this is resolved".
Ms Broadwell is, however, still being investigated by the Defence Department for allegedly mishandling classified information. FBI investigators found a "substantial amount" of material marked classified at her home.
The documents were part of her research from her trips to interview Gen Petraeus and his commanders across Afghanistan for her best-selling book on him, 'All In'.
Gen Petraeus told friends that he had never given classified information to Broadwell, and she said she didn't receive such material from him.
Gen Petreaus and Ms Broadwell say their romantic relationship began only after he retired from the military and started at the CIA.
Both Gen Petraeus (60) and Ms Broadwell (40) are married and Broadwell has two young children.
Gen Petraeus and Ms Broadwell have both expressed regret for the affair, which they say ended this summer.
The CIA is investigating Gen Petraeus' conduct to examine whether he may have used CIA resources to further the affair, but the Pentagon has shown no appetite for recalling Gen Petraeus to active duty in order to punish him for adultery, which is illegal under military law.
Ms Kelley befriended top military officers as part of her volunteer work hosting elaborate parties for Gen Petraeus and other top commanders at Central Command, a huge military base in Tampa.