Horn, 59, of the famed "Siegfried & Roy" animal and magic act, had been in intensive care at University Medical Center in Las Vegas until his transfer on Tuesday.
"Roy is now making the transition from survival to recovery," longtime partner Siegfried Fischbacher said Wednesday in a statement.
Horn was admitted for further evaluation and treatment, UCLA officials said. His condition was serious, but his vital signs were stable.
Horn was attacked Oct. 3 by one of the white tigers featured in the duo's show. Immediately after the attack, Horn reportedly said: "Don't harm the cat."
Fischbacher has suggested that the animal was trying to help Horn, but other animal experts disputed that.
The 7-year-old white tiger named Montecore has been released from quarantine.