Eric Garner's death in July 2014 was the first of a wave of high-profile, racially-charged incidents in the United States in which officers have been accused of using unreasonable force or being too quick to fire at black suspects.
US cop who killed unarmed black man guilty of rights charge
For years, the New York police held back from proceedings on the grounds that they had to wait until a federal civil rights investigation first ended.
But on Wednesday the Department of Justice conveyed that they had no objection to police moving forward, an official told AFP.
Proceedings would begin "in the coming days," against Officer Daniel Pantaleo and Sergeant Kizzy Adonis, a police official said. Internal administrative trials would likely not begin before next year, The New York Times reported.
Garner, 43, was wrestled to the ground for allegedly selling illegal cigarettes on New York's Staten Island.
Graphic cell phone footage, which went viral, showed the heavily built Garner, who had asthma, complaining "I can't breathe" 11 times.
He lost consciousness at the scene and was pronounced dead after being taken to the hospital. Chokeholds are outlawed by New York police.
The medical examiner's office classified Garner's death as a homicide but a grand jury refused to prosecute the white officer who deployed the fatal chokehold.
Violent protests in Chicago after man shot dead by police
Garner's death set off numerous protests in New York and elsewhere, magnified by the August 9, 2014 police shooting of unarmed black teenager Michael Brown in Ferguson, Missouri.
New York police subsequently began a pilot body-camera program, which they have since announced will be extended to all patrol officers and detectives by end-2018.
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