In a statement on his Twitter account, it was confirmed that the 15-time major winner had suffered "open fractures" to his lower right leg and ankle in the single-vehicle accident.
Additional injuries to his foot and ankle have been stabilised with screws and pins, it added.
“He is currently awake, responsive and recovering in hospital,” the statement went on.
“We thank everyone for the overwhelming support and messages during this tough time.”
According to the police, the 45-year-old had escaped lightly after needing to be “extricated from the wreckage” by firefighters following the crash early on Tuesday morning.
"I will say that it's very fortunate that Mr. Woods was able to come out of this alive,'' said Deputy Carlos Gonzalez, who first arrived on the scene.
The sheriff's department had said earlier that the “Jaws of Life” were used to pull Woods out to safety, but officials later said that was not the case.
A full assessment of the injuries sustained by Woods in the horror crash on a steep roadway in a suburb 30 miles south of downtown LA was delivered by Dr Anish Mahajan, the chief medical officer and interim CEO, of Harbor-UCLA Medical Center.
He said: "Comminuted open fractures affecting both the upper and lower portions of the tibia and fibula bones were stabilized by inserting a rod into the tibia.
"Additional injuries to the bones of the foot and ankle were stabilized 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."
Earlier, the full details of the crash had been outlined by Alex Villanueva of the Los Angeles County Sheriff's Department.
According to him, Woods was conscious and able to communicate with officials who arrived on the scene at approximately 7.18am local time following a 911 call from someone who lives near the crash site.
The LA County Fire Department chief, Daryl Osby, reported that Woods was in serious but stable condition upon arrival.
The authorities reported there was no immediate evidence that Woods was impaired in a check for a smell of alcohol or signs that he was under the influence of a substance at the scene.
According to the police, the car Woods was driving appeared to first make contact with the central reservation before careering across the two southbound lanes in a 45mph zone.
He then hit a pavement and some trees as the vehicle rolled over “several times” before coming to rest a fair distance from the road.
There were no skid marks and no evidence of braking, and, according to the police, the weather was not a factor.
Woods was in Los Angeles over the weekend as host of the Genesis Invitational at Riviera Country Club.
He is currently recovering from a fifth back procedure and admitted he is facing a race against time to be ready for the Masters in April.
According to reports, Woods had stayed on in LA for a two-day content shoot with Golf Digest/GOLFTV.