Odom was accompanied by his estranged wife, Khloe Kardashian, according to a statement from Alvina Alston, publicist for Odom's aunt JaNean Mercer. They left Las Vegas around 8 p.m. ET, and he was in a private room in a Los Angeles hospital later that night, sources told ESPN's Ramona Shelburne.
The family statement thanked the hospital and Odom's fans and said his father and his two children from a previous relationship are with him, along with Kardashian.
"He continues to make miraculous progress, taking a few steps in Los Angeles," the statement said.
Kardashian issued her own statement Tuesday thanking family, friends and fans for their "prayers and well wishes to Lamar" over an "incredibly difficult" week.She also thanked the staff at Sunrise Hospital in Las Vegas for their "kindness and diligent work," saying, "Under their amazing care, incredible strides have been made."
The helicopter for Monday night's move was large enough to transport the 6-foot-10 Odom, who had to be transported to Las Vegas by ambulance last week because he was too tall for the helicopter from a regional hospital in Pahrump, Nevada, near the brothel where he was found unresponsive.
Odom's family and friends said earlier Monday that his condition was improving. He has been hospitalized since Tuesday, when he was found at Nevada's Love Ranch brothel, 90 minutes northwest of Las Vegas. He was rushed to the hospital and put on life support.
Odom has been breathing on his own, without a tube, since Friday, according to sources. He also has been conversing with family and friends.
The 35-year-old former NBA standout has started physical therapy and will soon try to walk, sources told the Los Angeles Daily News.
Jim Harrick, Odom's college coach at Rhode Island, told CNN that Odom has made progress.
"We're more hopeful now," Harrick said. "We've been on pins and needles for days."
ESPN's Ramona Shelburne and The Associated Press contributed to this report.
Saunders: Why didn't anyone do something for Odom?
John Saunders asks where Lamar Odom's family and friends were in the lead-up to the situation in Nevada that has left him hospitalized.