The golfing legend was this week transferred to Cedars-Sinai Medical Centre in Los Angeles from Harbor UCLA Medical Centre, where he underwent surgery for his leg fractures on Wednesday.
In a brief message posted on social media, it has now been confirmed Woods, 45, has undergone multiple follow-up operations after sustaining "gruesome" leg injuries, including a shattered ankle and two leg fractures, after his car rolled near the side of a highway in Los Angeles on Wednesday.
"Tiger has moved to Cedars-Sinai Medical Centre and received follow-up procedures on his injuries this morning," the statement announced.
"The procedures were successful, and he is now recovering and in good spirits.
"Tiger and his family want to thank you all for the wonderful support and messages they have received over the past few days. We will not have any further updates at this time."
Meanwhile, police investigating the car crash may still request a blood sample from the golfing legend to definitively rule out drugs and alcohol being a factor in the accident, the Telegraph reported.
Detectives announced on Wednesday that the crash was "purely an accident" and that they did not anticipate criminal charges being brought against the 45-year-old, but they have been accused of jumping to conclusions too early and may now also request his telephone data to see if he was on the phone or otherwise distracted.
Alex Villanueva, the sheriff of Los Angeles County, said clues about the cause could come from Woods' wrecked vehicle.
"We're hoping there's going to be a black box and we'll have some information about the speed," Villanueva said. "It was maybe a factor in this accident."
Joe Giacalone, a professor at the John Jay College of Criminal Justice and a retired New York police sergeant, said it was "premature" for Villanueva to determine the crash was an accident just a day later.
"The blood test could give us a whole other insight," Giacalone said, noting that some drugs were not necessarily detectable by observation. "Because it's Tiger Woods, people are going to demand answers. You have to dot your I's and cross your T's."
A statement from Woods' representatives earlier this week explained in detail the first round of emergency surgery the 14-time major championship winner went through.
Anish Mahajan, MD, Chief Medical Officer and interim CEO of Harbor-UCLA Medical Centre, said in the statement Woods suffered compound fractures that resulted in bone fragments sticking through his skin.
"Mr Woods suffered significant orthopaedic injuries to his right lower extremity that were treated during emergency surgery by orthopaedic trauma specialists at Harbor-UCLA Medical Centre, a level 1 trauma centre," Dr Mahajan said.
"Comminuted open fractures affecting both the upper and lower portions of the tibia and fibula bones were stabilised by inserting a rod into the tibia. Additional injuries to the bones of the foot and ankle were stabilised with a combination of screws and pins. Trauma to the muscle and soft-tissue of the leg required surgical release of the covering of the muscles to relieve pressure due to swelling."
Woods' team added: "He is currently awake, responsive and recovering in his hospital room.
"Thank you to the wonderful doctors and hospital staff at Harbor-UCLA Medical Centre, the Los Angeles County Sheriff's Department, and the Fire Department. Your support and assistance has been outstanding."
Woods is reported to have said on Friday that he is not giving up hope of returning to the golf course.
Woods vowed not to let his car crash finish his career, reportedly telling friends: "It can't end like this."
He made the pledge as his girlfriend Erica Herman, agent Mark Steinberg and caddie Joe LaCava visited him at the medical centre in Los Angeles.
A source close to Tiger said the ace was "frustrated" and told People magazine: "He doesn't want his career to end like this.
"If there's any way at all he can continue playing, he will."
Authorities are still investigating the cause of the crash.
Woods has no memory of the accident and appeared to be unaware of how badly injured he was when the first deputy arrived at the scene, according to reports.
"At the hospital he was asked about it by the investigators and he had no recollection of the crash itself," LA County Sheriff Alex Villanueva told CNN.
