Redmond was arrested in January on drug charges while in rehab but vowed to Fawcett before her death that he would get sober.
In an appearance on the Today show, Redmond's father - and Fawcett's former partner - Ryan O'Neal said that his son followed through on his promise.
"He was thunderstruck to lose her," Ryan said.
"He turned his life around immediately."
He added: "I've never seen such focus and success. He's doing extremely well. I say that with pride. I'm extremely relieved and gratified with his progress in the last year. He's living in a sober living situation in Pasadena, and he's beautiful, and his mother would be so proud of him."
Fawcett died of anal cancer one year ago on June 25, 2009.