State District Judge Tammy Kemp also hugged her and gave her a Bible.
Brandt Jean, 18, said he was not speaking on behalf of his family but he himself did not want Amber Guygan to even go to prison.
Brandt's older brother Botham Jean was murdered last September aged 26 when Amber Guygan, 31, claims she walked into his unlocked flat, thinking it was her own, and shot him.
She lived on the floor below and thought he was an intruder, when he was actually sitting eating ice cream in his own flat.
Guyger was sentenced on Wednesday for 10 years, something Jean's mother has criticised saying it is not long enough.
Botham was an accountant for PwC but also lead Bible studies for the young adults in his church, Dallas West Church of Christ, and led worship at his Christian university.
Jessica Berry, a close friend of his and also a member of the church said shortly after his death: "It's like a big chunk of the church's heart has been ripped out."
Brandt Jean said in court: "I don't want to say twice or for the hundredth time how much you've taken from us, I think you know that but I just hope you go to God with all the guilt, all the bad things you may have done in the past.
"Each and every one of us may have done something that we're not supposed to do. If you truly are sorry, I know, I can speak for myself, I forgive you and I know if you go to God and ask him, he will forgive you.
"And I don't think anyone could say it, again, I'm speaking for myself not even on behalf of my family, but I love you just like anyone else and I'm not gonna say I hope you rot and die just like my brother did, but I personally want the best for you,
"I wasn't gonna ever say this in front of my family or anyone but 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 want you to do and the best would be giving your life to Christ.
"I'm not gonna say anything else. I think giving your life to Christ will be the best thing that Botham would want you to do. Again, I love you as a person. I don't wish anything bad on you.
"I don't know if this is possible, but can I give her a hug?"
"Yes" the judge replied and Jean crossed the court and was approached by a tearful Guyger who put her arms round his neck and he hugged her back.
On leaving, Guygen also received a hug from the judge, as well as a Bible and some advice to look at John 3:16 from Tammy Kemp.
BREAKING: In stunning moment, Botham Jean's brother embraces Amber Guyger after her sentencing for his brother's murder.— ABC News (@ABC) October 2, 2019
"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 want." https://t.co/sWaPUtS0kj pic.twitter.com/xPAIKQLh6z
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