The caser received international attention when Botham's brother told the police officer that God would forgive her if she was truly sorry and gave her a hug.
Prosecutors had asked jurors to sentence Amber Guyger to 28 years, which was how old her neighbour Botham Jean would have been if he was still alive.
Guyger said she mistook Mr Jean's apartment for her own and fatally shot him in his living room in September 2018.
One of the two jurors - a white man who was not named by ABC News - said the jury was moved by testimony from Mr Jean's family and friends, who described his deep faith and caring nature.
"We all agree that (the shooting) was a mistake, and I don't think Bo would want to take harsh vengeance," the juror said, referring to Jean by his nickname.
"I think he would want to forgive her."
After convicting Guyger of murder, the jury could have sentenced her to anywhere from two years to life in prison.
When the jury's 10-year sentence was handed down on Wednesday, a crowd outside the courtroom reacted angrily, believing it was too short.
A black woman on the jury told ABC News that her reaction when hearing prosecutors' sentencing request was "I can't give her 28 years".
"I know a lot of people are not happy about the 10 years," she said. "But I felt like... this case was not like any other case."
She drew distinctions between the death of Mr Jean and those of other unarmed black men who have been killed by police in recent years.
"Those officers that killed unarmed black men, when they got out, they went back to living their lives," she said.
"Amber Guyger, ever since she killed that man, she has not been the same. She showed remorse and that she's going to have to deal with that for the rest of her life."
On Friday, the Jean family stood with Dallas activists and religious leaders asking the US Department of Justice to conduct a broad probe of the Dallas Police Department.
Lee Merritt, a lawyer for the family, said at the news conference that Guyger's trial revealed that the city's police are incapable of investigating their own.
He called on police Chief Renee Hall to invite the Justice Department to do a "comprehensive audit" of her police force.
Guyger was transferred into the custody of the Texas Department of Criminal Justice on Friday, the Dallas County Sheriff's Department said.
During the sentencing, Mr Jean's brother addressed Guyger directly from the witness stand.
Brandt Jean told her that his brother would have wanted her to turn her life over to Christ, and that if she can ask God for forgiveness, she will get it.
"I love you as a person. I don't wish anything bad on you," he said to the 31-year-old Guyger, before adding, "I don't know if this is possible, but can I give her a hug?"
The judge said he could, and Mr Jean and Guyger stood up, met in front of the bench and embraced while Guyger cried.
Judge Tammy Kemp also hugged Guyger before she was led from the courtroom.
Dallas County District Attorney John Creuzot, a former trial judge, called Brandt Jean's embrace of Guyger "an amazing act of healing and forgiveness that is rare in today's society ... especially for many of our leaders".
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