Barry Jones is making up for almost three decades of lost time by reconnecting with family and friends after spending 29 years on death row.

Jones, 64, was released from an Arizona prison last week, just in time to celebrate Father's Day with his now-adult children, CNN affiliate KNXV reported. "It is an incredible feeling to be back in the arms of my family after 29 years," Jones said in a statement after his release.

"I am so grateful to my defense team who never gave up on exposing the truth in my case, and to my family who stood by me throughout this terrible ordeal," he added.

Jones is a free man after the state attorney general's office and Pima County attorney's office agreed his first-degree murder conviction should be vacated. He was offered a plea agreement on a second-degree murder charge which he accepted, the county attorney's office said in a statement.

That charge came with a 25-year sentence, and since Jones was given credit for the 29 years he had already served, he was released, the statement said.

Jones was convicted in 1995 of first-degree murder in the death of his girlfriend's 4-year-old daughter. The little girl died in 1994 in Pima County, Jones' paralegal, Jennifer Schneider, told CNN. He was sentenced to death in July 1995, CNN affiliate KTVK reported.

But evidence that would have shown that the child didn't sustain the internal injuries that caused her death while under Jones' care wasn't discovered by his trial attorney or his post-conviction attorney, according to the Death Penalty Information Center.

A reexamination of the medical evidence in the case "does not support a finding of proof beyond a reasonable doubt that Barry Lee Jones caused" those injuries, the Pima County attorney's office said in a statement last week. Evidence given at the trial did prove that Jones didn't take the child to the hospital the night before she died, despite seeing that she was sick from her injuries, KTVT reported.

"His (Jones') responsibility, and the extent of the responsibility, was that he should have recognized she needed care and taken her to the hospital, which is a far cry from where we were, which was that he caused the injuries, that he had spent the day abusing her," Andrew Sowards, a retired investigator with the Arizona Public Defender's Office told KTVT.

Sowards worked on Jones' case for 11 years, the station reported.

"We are profoundly grateful to the Arizona Attorney General and the Pima County Attorney for taking a fresh look at Mr. Jones's case and acknowledging he had never received a fair trial, just as the federal district court and the Ninth Circuit had previously found," Cary Sandman, a federal public defender whose office has represented Jones for over 20 years, said in a statement.

"We hope that Barry can enjoy the rest of his life in peace surrounded by his family and friends," the statement added.

Sowards has created a GoFundMe campaign to help get Jones on his feet as he reenters society.

"These are some of the most difficult decisions we face as prosecutors, trying to balance the rule of the law and in this case holding someone accountable for the death of an innocent 4-year-old child," Pima County Attorney Laura Conover said in a statement.

"What's also important is having the courage to reevaluate these cases thoroughly, while staying true to our responsibility of charging them accordingly with what is right in the eyes of the law. To that end Mr. Jones has been held more than accountable."

Jones' case is "one of thousands across the nation each year that continues to highlight the danger surrounding the death penalty," Conover told CNN in an emailed statement.