Cozart, 18, was ordered to jail during a hearing at the Skokie Courthouse, according to Cook County Sheriff's office spokeswoman Sophia Ansari. Cozart turned 18 in August, and this is his first stint in the jail.
Cozart was required to undergo random drug testing following a May 27 arrest in Northfield for driving 110 mph in his black 2011 BMW on the Edens Expy.
He pleaded guilty to the charge and paid a $531 fine. He was also ordered to serve 18 months probation and complete 60 hours of community service, in addition to the random drug tests.
Cozart posted a picture of himself outside the courthouse on his Instagram account Tuesday morning: "OutSide Da Court House Turnning Myself In."
Keef has served time in juvenile detention for pointing a gun at Chicago police officers. He was sent back to juvenile detention earlier this year for a violation of his parole for handling a firearm in a promotional video.
Keef, who grew up in Englewood, currently lives in Northbrook. He gained notoriety last year for a gloating tweet sent from his account after the slaying of a rival rapper.
The rapper was clocked at 110 mph, police say, as he drove home from a Davenport, Iowa, rap show just after 3 a.m. on a Monday.
Cozart told police he had $8,000 cash on him at the time of his arrest. When police are overheard showing Cozart how fast he was driving on their radar, he's heard responding, "It's a fast car, that's why I bought it." during the arrest, Cozart also handed an officer the insurance for an Audi, instead of the BMW he was driving.
Cozart was also charged with driving without a license because he only had a permit and had an unlawful number of passengers for a graduated driver.
The arrest came one week after being arrested in Georgia on a marijuana charge.
Cozart was stopped on the northbound Edens Expressway in a 55 mph zone from Lake Avenue to Tower Road in the north suburb.
Cozart, who listed a Northbrook address, had three passengers with him in his 2011 BMW when he was stopped.
He was booked into jail May 20 after an arrest at a hotel in Dunwoody, Ga., after hotel security "observed smoke and a smell of marijuana from a room."
The rapper posted a mugshot of himself May 21 on Instagram and announced on Twitter that he "Jus Got Out" of jail in DeKalb County, Ga.
The Sun-Times Media Wire contributed to this report.