Jackson was executed by lethal injection and pronounced dead at 6:13 p.m. EDT at the Mississippi State Penitentiary in Parchman, The (Jackson) Clarion-Ledger reported.
Jackson's sister, Regina Jackson, had met with Bryant Monday to ask that her brother not be put to death, the newspaper said.
Jackson was convicted of killing 2-year-old Shunterica Lonnett Jackson, 5-year-old Dominique Devro Jackson, 3-year-old Antonio Terrell Jackson and 2-year-old Andrew Odutola Kuyoro Jr. during a rampage in 1990. Authorities said the slayings took place while he was searching for money in a safe at his mother's home near Greenwood. He was also convicted of aggravated assault on his sister and another niece.