Jabari Edwards, 28, has been charged with two felony counts of attempted first-degree murder.
Edwards was apprehended in Burlington, Iowa and was extradited back to Chicago earlier this month, police say.
"This arrest is a result of exceptional police work," Brown said. "It should serve as a warning to all those involved in criminal activity that you cannot run, nor can you hide from justice."
Officer Fernanda Ballesteros was shot as she and her partner were attempting a traffic stop around 5:42 p.m. on June 1 near 61st Street and S. Paulina, Supt. David Brown said.
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The car they were attempting to stop at first sped off, Brown said, then came back around and slowed down so they could pull up parallel to the officers' car. Then, someone opened fire, striking the female officer, who was the driver of the squad car.
"They never completed the traffic stop. They saw the offenders do something at 61st Street, and they were following them," said 15th Ward Alderman Ray Lopez, who represents the ward where the shooting occurred and where the wounded officer's family lives.
"Then, as they were following them, the offender's vehicle turned, being almost perpendicular to the police officers' car, and then started shooting," he said, citing information he received from high-ranking police.
Ballesteros' partner jumped into the driver's seat and rushed her to University of Chicago Hospital, Brown said.
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The injured officer's partner was also checked out at Northwestern and then released, with officials saying he was not injured in any way.
At the time, Ballesteros shared a message from her hospital bed.
"Most importantly, thank you to Officer Young, my partner, who had my back and carried me to safety. I'm forever grateful for his quick thinking and swift response. You were my guardian angel that night," she said. "I am choosing to see the light in this dark, and I will grow stronger, both physically and mentally, from this tragedy."
Ballesteros was released from the hospital five days after the shooting. She stood and tearfully waved to the officers who came to see her off, as her partner helped her in a wheelchair.
She got out of that wheelchair to hug Officer Carlos Yanez, who was seriously wounded when his partner, Ella French, was killed in a shooting in the same neighborhood last summer.
Ballesteros is one of 27 Chicago Police Officers that have been shot this year, according to the CPD.