In a statement issued Friday, Odom's maternal aunt, JaNean Mercer, announced Odom's "transition to the next stage of his miraculous recovery at a new facility."
"Lamar continues to make remarkable strides," said Mercer, "and we are asking that you continue to respect our privacy. Again we THANK ALL OF YOU GREATLY, your support has been paramount in helping to uplift us during these past few difficult months."
Odom was released from the hospital earlier this week, family spokeswoman Alvina Alston said Friday, The Associated Press reported.
Odom, 36, was rushed to a Nevada hospital this past October after he was found unconscious at a legal brothel. Three days later, he opened his eyes, according to friends and family, and soon after, he was moved to a facility in Los Angeles.
His estranged wife, Khloé Kardashian, remained by his side throughout the ordeal.
"[Lamar's] doing amazing and I'm so proud of the strength that he has to fight this battle," Kardashian said on Wednesday. "Because it's not my story to tell, I try to respect that, and I want him to be able to tell that story. I'm just there to support and care for him."
Kayna Whitworth and The Associated Press contributed to this report.