Woods, who was involved in a serious car accident on Tuesday near Los Angeles, is "responsive, and recovering in his hospital room," the statement said.
Woods suffered serious leg injuries and was trapped but conscious when emergency responders reached the scene of his one-vehicle rollover crash on a stretch of California road known for speeding and accidents, authorities said Tuesday.
Woods, 45, was driving shortly after 7 a.m. PT in Rancho Palos Verdes, near Los Angeles, when the SUV he was using crossed a median and went across two lanes of road before hitting a curb, hitting a tree and landing on its side off the roadway in the brush.
A Los Angeles County sheriff's deputy who was the first to arrive said he found Woods still in the driver's seat, wearing his seatbelt, and that the golfer was able to tell him his name was Tiger.
The 15-time major champion was lucid and calm, but potentially in shock, and didn't seem to be concerned with his injuries at the time, Deputy Carlos Gonzalez said.
Los Angeles County Fire Chief Daryl Osby told CNN's John Berman that Woods was alert and oriented and was trying to "self-extricate" but he was stuck.
Firefighters used a pry bar and an ax to free the golfer, who this past weekend hosted a PGA Tour event in the area but didn't play because of a recent back surgery.
They broke the windshield with the ax and used the bar to pry the seats and metal from around Woods' legs, Osby said.
They put Woods in a neck collar, attached leg splints and used a backboard to get him through the giant hole in the windshield to an ambulance. He went to the hospital in serious but stable condition with injuries to both legs, Osby said.
Woods' agent, Mark Steinberg, said the golfer was in surgery with multiple injuries, according to Golf Digest.
How the crash happened
The crash, which destroyed the front of the Genesis SUV courtesy vehicle, could have been fatal, but the airbags and seatbelts helped Woods survive, Gonzalez and Sheriff Alex Villanueva said.
The sheriff said he thinks Woods was traveling at a high rate of speed down a hilly part of the road when the crash occurred.
There were no skid marks or other indications of braking, Villanueva added.
Villanueva said that section of road is "downhill on a curve," and he and Gonzalez said the area is known as a trouble spot for speeding and accidents.
Deputies responding to Woods saw no evidence of impairment, Villanueva said, and they didn't ask hospital officials to take a blood draw, he said.
A Los Angeles law enforcement source told CNN that no field sobriety test was administered because of the seriousness of Woods' injuries.
A tweet from the sheriff's department earlier said rescuers used the Jaws of Life to get Woods out of the vehicle, but Osby said firefighters in fact used a tool for prying and an ax to remove the windshield and free Woods.
Woods was taken to Harbor-UCLA Medical Center, a trauma center. CNN has reached out to the hospital for his condition.
The sheriff's department said Woods was the only occupant of the car.
Another car, not involved in the initial rollover incident, stopped after the crash and was rear-ended, according to Los Angeles County PIO Henry Narvaez.
The days leading up to the crash
Woods likely was headed for the Rolling Hills Country Club in nearby Rolling HIlls Estates for a shoot with Golf Digest and Golf TV, according to Daniel Rapaport, the Tiger Woods correspondent for Golf Digest.
Woods had a 7:30 a.m. call time, with shooting supposed to begin around 8. It was the second day of shooting.
Rapaport told CNN's "Situation Room with Wolf Blitzer" that Woods was not playing or hitting, but was giving on-course playing lessons to celebrities.
"He was in good spirits on Monday when he did that," Rapaport said of the shoot.
Woods had hosted the Genesis Invitational over the weekend, and was seen intermittently on Saturday and more often during Sunday's final round.
Woods was at the course Monday with NBA legend Dwyane Wade, actress Jada Pinkett Smith and actor David Spade.
"The reason I picked up a golf club. Yesterday was a pretty cool day! Thank you @tigerwoods @golfdigest for this dope opportunity!" Wade wrote on Instagram Tuesday.
Smith posted photos on Twitter of her and Woods at the links.
"Guess who I had the most awesome golf day with yesterdayyyyyy??? Yes! The magnificent @TigerWoods !!!! Yes ... dreams come true. I can't wait for you to see my golf journey with Tiger. Stay tuned!" she wrote.
Spade joked about Woods' ability as an instructor.
"Golf lesson with this guy today. And you know what? He's not bad... He picks things up very quickly. Good listener," he tweeted with a photo of himself and a smiling Woods.
Woods, who has won a record-tying 82 PGA Tour events, announced earlier this year that he had a recent back operation, the fifth of his professional career.
Woods told CBS sportscaster Jim Nantz in video posted Sunday on the PGA Tour's Twitter feed that he was "feeling fine" but a "little bit stiff" after his most recent procedure. He said he was scheduled to get one more MRI.
Woods previously had back surgery -- a spinal fusion -- in 2017 and made his return almost a year later. He went on to launch a remarkable comeback, winning the Masters in 2019.
Any progress last year was hampered by yet another back injury and the pandemic, which heavily disrupted the golf calendar.
"We have been made aware of Tiger Woods' car accident today. We are awaiting further information when he comes out of surgery. On behalf of the PGA TOUR and our players, Tiger is in our prayers and will have our full support as he recovers," PGA Tour Commissioner Jay Monahan said
Woods last played competitive golf at the rescheduled Masters in November. He also played golf in a father-son event called the PNC Challenge in December in Florida.
Woods was the host of this weekend's PGA Tour event, the Genesis Invitational at Riviera Country Club in Pacific Palisades, and some proceeds went to his foundation.
World No. 3 golfer and friend Justin Thomas got emotional while talking about Woods ahead of the Workday Championship at The Concession event in Bradenton, Florida.
"I'm sick to my stomach," he told PGA Tour Entertainment. "You know, it hurts to see one of your -- now one of my closest friends get in an accident. Man, I just hope he's all right. Just worry for his kids, you know. I'm sure they're struggling."
Jack Nicklaus, whose record of 18 major titles Woods has been chasing, tweeted his well wishes.
"Barbara and I just heard about Tiger's accident, and like everyone else, we are deeply concerned," he wrote. "We want to offer him our heartfelt support and prayers at this difficult time. Please join us in wishing Tiger a successful surgery and all the best for a full recovery."
Corrections: This story has been updated with the correct status of Woods' vehicle as well as the correct spelling of the Los Angeles County spokesperson's last name. Also, the LA County Sheriff's Department initially said Woods was cut from his vehicle using the Jaws of Life. It has since said that is not the case. This story has been updated to reflect that.
CNN's Stella Chan and Cheri Mossburg reported from Los Angeles and Steve Almasy reported and wrote from Atlanta. CNN's Paul Vercammen, Andy Rose, David Close, Kevin Dotson and Dan Moriarty contributed to this report.