"He knows he is very lucky to be alive," a source tells PEOPLE of Tiger Woods, who was involved in a single-vehicle crash last month
tiger woods
Tiger Woods

Tiger Woods is focused on his recovery. 

The golfer, 45, shared on Tuesday that he was back home in Florida after undergoing emergency surgery for "significant orthopedic injuries to his right lower extremity" that he suffered in a single-vehicle rollover car crash in California last month. 

"Tiger is happy to be back home," a source tells PEOPLE of Woods, who spent almost three weeks in the hospital. "He is still recovering and has some pain, but he is in good spirits."

"He is focused on his continued recovery. There is a rehabilitation plan that he is focused on. He knows he is very lucky to be alive," the source adds. "He appreciates that he has access to great medical care. He has a great attitude and is just focused on his recovery."

Woods was also "excited" to be reunited with his children, son Charlie Axel, 12, and daughter Sam Alexis, 13. 

"He has spent some time with his kids," the source says. "They stayed in touch while he was in the hospital, but he was excited to see them in person."

tiger woods
Tiger Woods (center) with his children and girlfriend Erica Herman

In a statement shared on social media this week, Woods wrote that he was "happy to report that I am back home and continuing my recovery."

"Thank you to the incredible surgeons, doctors, nurses and staff at Harbor-UCLA Medical Center and Cedars-Sinai Medical Center," the father of two added. "You have all taken such great care of me and I cannot thank you enough. I will be recovering at home and working on getting stronger every day." 

RELATED VIDEO: Tiger Woods 'Awake,' 'Responsive and Recovering' After Car Accident in California

Woods was involved in a single-vehicle crash on the morning of Feb. 23 in California.

Woods was traveling downhill when his car struck a sign in the center divider, sheared through a tree and landed in the brush alongside the road with major damage, according to the Los Angeles County Sheriff's Department.

Following the crash, Woods was hospitalized and underwent emergency surgery.

Want to get the biggest stories from PEOPLE every weekday? Subscribe to our new podcast, PEOPLE Every Day, to get the essential celebrity, entertainment and human interest news stories Monday through Friday.

Tiger Woods
Tiger Woods
| Credit: Patrick Smith/Getty

On Saturday, TMZ reported that investigators have not found any evidence that Woods took his foot off the gas or did anything to prevent the crash once he lost control of the vehicle.

The Los Angeles Sheriff's Department told PEOPLE in a statement that the "investigation is ongoing and we do not have that information. As soon as we have more information, it will be released." 

Earlier this month, new details regarding the rollover crash surfaced in a Los Angeles County affidavit for a search warrant of his vehicle's black box.

According to the documents obtained by CNN, Woods told police following the crash that he had no recollection of driving or how the accident happened. Woods was also unconscious at some point after the accident, according to the affidavit, although he was conscious when sheriff's deputies arrived.  

Deputy Johann Schloegl, the traffic collision investigator on the case, wrote in the affidavit that a witness who heard the crash noticed Woods was "unconscious and not responding to his questions" when they first approached the scene of the crash, according to CNN.