Staten Island District Attorney Daniel Donovan said a court granted his request Monday to impanel the grand jury. Donovan said it will begin work next month.
Eric Garner, 43, died in mid-July as police arrested him for allegedly selling loose cigarettes on the street. A video from a cellphone shows an officer, identified as Daniel Pantaleo, holding Garner in a chokehold -- something New York police have been banned from using for years.
A medical examiner ruled Aug. 1 that the death was a homicide.
Donovan said he is unsure how long the investigation will take.
"I will make no comment now, or during the period of time that the Grand Jury is convened, regarding the days that the Grand Jury will be sitting; who may be called as a witness before the Grand Jury; what any witness has or will testify about before the Grand Jury; when the Grand Jury will conclude its investigation; what criminal charges will be considered by the Grand Jury, or against whom the Grand Jury might consider any such criminal charges."
Police have said that Garner, a father of six, resisted arrest July 17, and that he died of cardiac arrest. But the video, taken by a bystander, shows him saying, "I can't breathe," as he is held down.
The death sparked protest marches. The Rev. Al Sharpton, who has led many of the demonstrations, has demanded Pantaleo's arrest and a federal investigation.
Donovan said he has devoted more resources to the investigation than to any other during his time as district attorney, with six assistant district attorneys and 10 investigators working on the case.