In an incredible act of compassion, the brother of the black man murdered by white Dallas cop Amber Guyger hugged her and offered her forgiveness Wednesday as she was sentenced to 10 years behind bars.

Victim Botham Jean’s brother, Brandt Jean, was reading a victim-impact statement in the Texas courtroom when he broke off and asked the judge if he could hug Guyger.

“I don’t know if this is possible, but can I give her a hug, please? Please?” Jean asked Judge Tammy Kemp.

The jurist said yes, and Brandt got off the stand and walked toward Guyger at the defense table. She leaped up from her seat and ran to hug him.

They clutched each other in an embrace that lasted for more than a minute — with Guyger loudly sobbing into Jean’s shoulder.

At one point Kemp also embraced Guyger and gave her a Bible.

The 31-year-old former cop had just been sentenced to a decade in prison for fatally shooting Botham Jean, 26, after she entered his apartment, mistaking it for her own one floor below.

She was allegedly distracted while sexting her cop boyfriend when she made the fatal mistake as she returned home after work.

Botham was eating a bowl of ice cream in his apartment, which was unlocked, when Guyger shot him, thinking he was an intruder at her place.

Her lawyers said the killing was just a tragic error. Prosecutors said she should have called for back-up before shooting anyone — and suggested she had a racist past.

Either way, her victim’s brother said in court that he didn’t think she should do any time.

“I don’t even want you to go to jail. I want the best for you because I know that’s exactly what Botham would do,” he said.

Guyger had faced a sentence of five to 99 years on the murder rap. Before her guilty verdict was rendered by a jury Tuesday, she elected for the panel also to decide her sentence.

Prosecutors asked for no less than a 28-year sentence in honor of Botham, who would have turned 28 last month.

In pushing for a stiff sentence, the prosecution brought up text messages that had sent before the slaying Sept. 6, 2018.

In some of the texts, the then-cop joked about Martin Luther King Jr.’s assassination while working security at a parade in his honor last year.

Her friend texted her, “When does this end lol.’’

Guyger responded, “When MLK is dead. . . oh wait . . .”

The messages were deleted but later retrieved by authorities.

After her guilty verdict was announced in court Tuesday, shouts of “Black lives matter!’’ erupted in the street outside.

During her time on the stand, Guyger said she wished Botham “had the gun and killed me.’’

The jury convicted her after deliberating for just five hours.

After the verdict, Guyger remained standing until the jurors filed out of court. Then she collapsed back in her seat and stayed there for about 15 minutes before guards led her away.

She is not eligible for parole.