Woods had to be cut from the vehicle with the "jaws of life" tools, the Los Angeles County Sheriff's Department said in a statement.
Deputy Carlos Gonzalez, the first officer on the scene, told a press conference: "I will say that it's very fortunate that Mr Woods was able to come out of this alive.”
The sheriff said that he sometimes catches people topping 80 mph in the 45 mph zone and has seen fatal crashes there.
The golf superstar had to be pulled out through the windshield, and his agent said he was undergoing leg surgery.
Woods, a 15-time major champion who shares with Sam Snead the PGA Tour record of 82 career victories, was alone in the SUV when it crashed.
The vehicle crossed two oncoming lanes and rolled several times, authorities said at a news conference.
No other cars were involved.
The 45-year-old was alert and able to communicate as firefighters pried open the front windshield to get him out, officers said.
The airbags deployed, and the inside of the car stayed basically intact and that "gave him a cushion to survive the crash," Los Angeles County Sheriff Alex Villanueva said.
Both of his legs were seriously injured, county Fire Chief Daryl Osby said.
Officials said there was no immediate evidence that Woods was impaired.
Authorities said they checked for any odour of alcohol and other signs he was under the influence of a substance and did not find any.
They did not say how fast he was driving.
The crash happened on a sweeping, downhill stretch of a two-lane road through upscale Los Angeles suburbs.
Woods was in Los Angeles over the weekend as the tournament host of the Genesis Invitational at Riviera Country Club, where he presented the trophy on Sunday.
He was to spend Monday and Tuesday filming with Discovery-owned GOLFTV, with whom he has an endorsement.
A tweet on Monday showed Woods in a cart smiling with comedian David Spade.
Golf lesson with this guy today. And you know what? He’s not bad… He picks things up very quickly. Good listener pic.twitter.com/KinEAGcEKU
— David Spade (@DavidSpade) February 23, 2021
According to Golf Digest, also owned by Discovery, the TV shoot was on-course lessons for celebrities, such as Spade and Dwyane Wade, at Rolling Hills Country Club.
Woods has been recovering from surgery on his lower back in December.
It was his fifth back surgery and first since his lower spine was fused in April 2017, allowing him to stage a remarkable comeback that culminated with his fifth Masters title in 2019.
He has carried the sport since his record-setting Masters victory in 1997 when he was 21, winning at the most prolific rate in modern PGA Tour history.
He is thought to be responsible for TV ratings spiking, which has led to enormous increases in prize money during his career.
Even at 45, he remains the biggest draw in the sport.
The SUV he was driving on Tuesday had tournament logos on the side door, indicating it was a courtesy car for players at the Genesis Invitational.
Tournament director Mike Antolini did not immediately respond to a request for comment.
It is not unusual for players to keep courtesy cars a few days after the event.
Woods feared he would never play again until the 2017 fusion surgery.
He returned to win the Tour Championship to close out the 2018 season and won the Masters in April 2019 for the fifth time.
He last played December 20 in the PNC Championship in Orlando, Florida, an unofficial event where players are paired with parents or children.
He played with his son, Charlie, who is now 12. Woods also has a 13-year-old daughter.
During the Sunday telecast on CBS from the golf tournament, Woods was asked about playing the Masters on April 8-11 and said, "God, I hope so."
He said he was feeling a little stiff and had one more test to see if he was ready for more activities.
He was not sure when he would play again.
Celebrities all over the world have shared messages of support.
Actress and talk show host Pinkett Smith, 49, who had been playing golf with Woods the day before as part of a promotional project, shared a message on Twitter.
She said: “Prayers up for the GOAT @TigerWoods who was in an accident this morning. Was just with him yesterday.
“Don’t take not even a MOMENT for granted! I know you’re good because your Tiger within is a beast!!!”
Prayers up for the GOAT @TigerWoods who was in an accident this morning. Was just with him yesterday. Don’t take not even a MOMENT for granted! I know you’re good because your Tiger within is a beast!!!
— Jada Pinkett Smith (@jadapsmith) February 23, 2021
US singer and actress Cher, 74, shared two prayer hand emojis and wrote: “Saying prayers For Tiger Woods.”
Former baseball player Alex Rodriguez, 45, wrote: “Praying for my brother @TigerWoods as we all anxiously await more news.
“Thinking of him and his entire family.”
Match Of The Day host Gary Lineker, 60, added: “Thoughts are with @TigerWoods. Hope it’s not as serious as appears.”
Thoughts are with @TigerWoods. Hope it’s not as serious as appears. 🤞🏻🤞🏻
— Gary Lineker 💙 (@GaryLineker) February 23, 2021
"I'm sick to my stomach," Justin Thomas, the Number 3 golf player in the world, said from the Workday Championship in Bradenton, Florida.
"It hurts to see one of my closest friends get in an accident. Man, I just hope he's all right."
Crews used a crane to lift the damaged SUV out of the hillside brush.
The vehicle was placed upright on the street and sheriff's investigators inspected it and took photos.
Then it was loaded onto a flatbed truck and hauled away Tuesday afternoon.
This is the third time Woods has been involved in a car investigation.
The most notorious was the early morning after Thanksgiving in 2009, when his SUV ran over a fire hydrant and hit a tree.
That was the start of shocking revelations that he had been cheating on his wife with multiple women.
Woods lost major corporate sponsorships, went to a rehabilitation clinic in Mississippi and did not return to golf for five months.
In May 2017, Florida police found him asleep behind the wheel of a car parked awkwardly on the side of the road.
He was arrested on a DUI charge and said later he had an unexpected reaction to prescription medicine for his back pain.
Woods later pleaded guilty to reckless driving and checked into a clinic to get help with prescription medication and a sleep disorder.
Woods has not won since the Zozo Championship in Japan in fall 2019, and he has reduced his playing schedule in recent years because of injuries.
The surgery on Tuesday would be his 10th.
He has had four previous surgeries on his left knee, including a major reconstruction after he won the 2008 US Open, and five surgeries on his back.