I'm guessing there was no deathbed confession.
Probably not, but his 2006 "IF I did it," book tour interview video is pretty much confirmation that he did it. That confession, subject to body language analysis, is way more "beyond a reasonable doubt," information than even a non-biased jury's finding after a trial.
The words are literally coming out of his mouth. He's testifying. He's just couching it in "this is all hypothetical." But his body language pretty clearly indicates it's from memory.
On top of that he's also pretty clear that he had an accomplice with him that was never caught, and it was probably Charlie Erlich, the man who was later with him (and went to jail with him) in Las Vegas when OJ was arrested for burglary.