"I apologize for bringing any pain and hurt on anybody for the actions that I have caused to you all," Muhammad said after the sentencing.
According to the Dallas Morning News, Muhammad drowned 5-year-old Naim and 3-year-old Elijah to get back at their mother for leaving him.
In 2011, he abducted the boys and their mother, Kametra Sampson, as they walked Naim to his first day of kindergarten. Sampson escaped and called for help, but Muhammad asked the boys to pretend they were swimming and held them under creek water until they drowned.
"You've shown that you have no boundaries, that nothing is sacred to you -- not even the bond between a father and son," Sampson said.
In an attempt to garner Muhammad a life sentence without parole, his attorney argued that he was "not evil but he has committed an evil act.” He said Muhammad had grown up in a violent and sexually abusive home with a mother who was a crack-addicted prostitute.
"It was the ultimate textbook family violence power and control play -- 'If I can't get you to do what I want you to do through violence, I will go to your very heartstrings,'" a prosecutor said of Muhammad's actions.
It took the jury less than 10 minutes to convict him, but three and a half hours to sentence Muhammad to death.