Roy Oliver turned himself in after the warrant was issued on Friday, the Dallas County Sheriff’s Department said.
In a statement, the sheriff’s office cited evidence that suggested Oliver “intended to cause serious bodily injury and commit an act clearly dangerous to human life that caused the death”.
Oliver, 37, fired a rifle at a car of teenagers leaving a party, striking and killing Edwards.
The shooting led to protests calling for Oliver to be charged. About 200 people attended a vigil on Thursday night in Balch Springs.
Oliver was fired on Tuesday for violating department policies.
The shooting, which took place in a primarily black and Hispanic neighbourhood, stoked simmering tensions of perceived racial bias in US policing.
Edwards and his two brothers and two other teenagers were driving away from an unruly house party in Balch Springs late on Saturday night when Oliver opened fire on their vehicle.
The bullets shattered the front passenger-side window and struck Edwards.
Balch Springs police said officers were responding to a disturbance and heard multiple gunshots. They came across the vehicle with the teens and ordered it to stop, but it pulled away.
Police initially said the car Edwards was in was backing towards a police officer but Chief Jonathan Haber reversed his statement after viewing police video, stating that the car was driving away from the officer when he fired a rifle at the vehicle, fatally wounding Edwards.
Records show that Oliver was briefly suspended in 2013 following a complaint about his conduct while serving as a witness in a drunken-driving case.
Personnel records from the Balch Springs Police Department obtained by The Associated Press show Oliver was suspended for 16 hours in December 2013 after the Dallas County District Attorney’s Office filed the complaint.
Oliver also was ordered to take training courses in anger management and courtroom demeanour and testimony.
The personnel records also included periodic evaluations that noted at least one instance when Oliver was reprimanded for being “disrespectful to a civilian on a call”.
That evaluation, dated January 27, 2017, called the reprimand an isolated incident and urged Oliver to be mindful of his leadership role in the department.
The complaint from the prosecutor’s office said the office had a hard time getting Oliver to attend the trial, he was angry he had to be there, he used vulgar language that caused an assistant district attorney to send a female intern out of the room, and he used profanity during his testimony.
Oliver joined the Balch Springs department in 2011 after being an officer with the Dalworthington Gardens Police Department for almost a year.
Oliver has also served in the army, rising to the rank of sergeant while serving two tours in Iraq and earning various commendations.