The 42-year-old’s victory in Atlanta was his 80th PGA Tour title – only fellow American Sam Snead has more – but his first since August 2013.
Less than a year ago he was 1,199 in the world after spinal fusion surgery – the latest of multiple operations.
“I was having a hard time not crying on that last hole,” Woods said.
“I just can’t believe I’ve pulled this off.”
Thousands of fans spilled on to the 18th fairway to follow Woods to the green chanting “U-S-A” and “Tiger, Tiger” after his approach found a bunker on the edge of the green.
Woods holed out for par to complete a final round of 71 for an 11-under total before holding his arms aloft in celebration of a brilliant win just days before the Ryder Cup gets under way in Paris.
England’s Justin Rose lost his world number one ranking as a result of finishing tied fourth but secured the overall FedEx Cup which determines the season-long PGA Tour champion – the first Englishman to do so.
Rose birdied the 18th at East Lake for a 73 to finish on six under and seal the top-five finish he needed to win the $10m (£7.6m) bonus on offer as FedEx Cup champion.
‘I loved every bit of it’
Woods, who was two clear of compatriot Billy Horschel, said: “I had to suck it up and hit some shots. Once I got the ball on the green, it was done. I could handle it from there.”
The 14-time major champion’s last tournament victory was in August 2013 at the WGC-Bridgestone Invitational, since when he has had surgery on his back four times
“It was just a grind out there,” Woods added. “I loved every bit of it, the fight, the grind and the tough conditions.
“At the beginning of the year, it was a tall order but as the year progressed and I proved I could play, I knew I could do it again.”
He came into the final day of the tournament – the last of four FedEx Cup play-off events – with a three-shot lead over Rose and Northern Ireland’s Rory McIlroy, who faded from contention with a 74 to finish on five under in a tie for seventh.
Woods birdied his first hole – one of two birdies and three bogeys – with his place at the top of the leaderboard in little danger during the final round.
“It’s been tough. I’ve had a not-so-easy last couple of years,” he said. “I’ve worked my way back. I couldn’t have done it without the help of all the people around me.
“Some of the other players knew what I was struggling with. It was really special to see them at the green on 18. It’s just hard to believe I won the Tour Championship.”
‘He’s looked world class again’
The win for Woods, who is part of the United States team for next week’s Ryder Cup in Paris, means he is now two short of Snead’s all-time PGA Tour title record of 82.
It comes less than a year since Woods said he might never return to competitive golf following multiple back operations.
In April 2017 he had his third surgery in 19 months to try and cure pain in his back and leg.
He returned to competitive golf in November 2017 and admitted he was “winging it” as he waited to see if his back would hold up.
“I’ve been in bed for about two years and haven’t been able to do much,” Woods said before the Hero World Challenge, where he would finish ninth in the 18-man field.
Back on the PGA Tour in 2018, Woods missed the cut in his second event but crucially felt fit enough to add tournaments to his schedule and the results soon followed, most notably when he led the Open Championship at Carnoustie with eight holes to play and then finished runner-up in the US PGA Championship.
“All year long he’s looked like winning,” said Rose about Woods. “He’s played some great golf and he’s looked world class again.
“It was just a matter of time and I’m so happy for him.”
Rose nearly ‘throws it away’
Rose – whose one PGA Tour victory in 2018 came at the Forth Worth Invitational in May – entered the FedEx Cup play-offs fourth in the points list behind Dustin Johnson, Justin Thomas and Brooks Koepka.
After missing the cut at the opening Northern Trust tournament, he finished second in both the Dell Technologies Championship and the BMW Championship.
Rose, Tony Finau, Johnson, Bryson DeChambeau, defending champion Thomas and Woods all came into the Tour Championship with a chance to win the FedEx Cup bonus with a victory at East Lake.
With Woods looking certain to win the tournament, a top-five finish for Rose was going to be enough for the world number one to claim the overall title.
However, bogeys on the 11th, 14th and 16th saw Rose slip out of the top five and Woods was set to secure the FedEx Cup in addition to the Tour Championship.
Rose, 38, needed a birdie on the par-five 18th to finish joint fourth with Japan’s Hideki Matsuyama and claim the title.
“I was waiting for a break all day and to get it on the last hole was great timing,” said Rose, a European Ryder Cup team member. “I felt more pressure as I was throwing it away. It was a horrible scenario but fortunately I clicked into gear at the right time.
“Today is going to take a lot of absorbing but I can’t wait to go over to Paris.”
‘The greatest comeback of all time’ – reaction
English world number 12 Tommy Fleetwood: “Everybody watching at home, everybody that was right there when it happened. We’ve just witnessed the greatest comeback of all time! What a time to be alive!!!”
18-time major champion Jack Nicklaus: “I never dreamed Tiger Woods could come back and swing the way he has, after surgery. I think you could argue he’s swinging better than he has ever in his life. He has played fantastically! I think throughout this year some of Tiger Woods’ issues were between his ears, as he had to remember how to win again. Tiger has been close, almost there. You knew he was going to win soon, and this week he did it.”
His difficult decade
In October 2017 Woods, who last won a major in 2008, was sentenced to a year’s probation after pleading guilty to reckless driving.
He was arrested in May that year after officers found him slumped at the wheel of his parked Mercedes-Benz not far from his Florida home.
Woods insisted that alcohol was not a factor, which the toxicology test showed to be true.
He claimed his disorientated condition was caused by an unexpected reaction to the combination of medications he was taking, after surgery on his back.
In total he had four surgeries on his back in four years, at one point saying he simply wanted to be able to walk and live a normal life again after years of chronic pain.
In 2009 Woods was involved in a bizarre car crash outside his Orlando home.
The incident sparked accusations of extramarital affairs which led to the end of his seven-year marriage and the loss of lucrative sponsorship deals.
When Woods last won a tournament in August 2013…
Barack Obama was in the first year of his second four-year term as US President.
Manchester United were preparing to begin their first season under new manager David Moyes following the retirement of Sir Alex Ferguson.
British boxer Anthony Joshua had only just turned professional a month earlier, going onto become IBF, WBO and WBA world heavyweight champion.
Woods was still number one until May 2014. Seven players have held the position since – Adam Scott, Rory McIlroy, Jordan Spieth, Jason Day, Dustin Johnson, Justin Thomas and Justin Rose.
Of the 21 men’s major golf championships played since, there have been 16 different winners.
Tiger Woods career timeline
April 1997: Wins his first major championship at the Masters
June 1997: Becomes world number one for the first time, less than a year after turning professional
June 2000: Wins the US Open by a record 15 shots
June 2008: Wins his 14th major championship at the US Open to move within four of Jack Nicklaus’s record of 18
November 2009: His car hits a tree and fire hydrant outside his Florida home, leading to revelations about what he calls “transgressions” in his private life
August 2010: He and wife Elin Nordegren announce they are divorced
August 2013: Wins his 106th global title and 79th on the PGA Tour at the WGC Bridgestone Invitational
May 2016: Falls out of the top 500 in the world rankings for the first time as a professional, eventually reaching as low as number 1,199 in December 2017
April 2017: Has spinal fusion surgery, the third surgery in 19 months to try and cure pain in his back and leg
May 2017: Is arrested and charged with driving under the influence after being found asleep at the wheel of his car with the engine running.
September 2018: Is named as a wildcard pick for the 2018 Ryder Cup to return to the side for the first time since 2012, a month after finishing second at the PGA Championship.
Tour Championship final-round leaderboard (US unless stated)
-11 T Woods; -9 B Horschel; -7 D Johnson; -6 H Matsuyama (Jpn), W Simpson, J Rose (Eng); -5 R Fowler, J Thomas, X Schauffele, R McIlroy (NI)
Selected others: -4 T Fleetwood (Eng), P Casey (Eng); -3 T Finau; -1 B DeChambeau; +13 P Mickelson