He shot an 11-under-par 269 to bring home the $1.62 million prize in his first PGA Tour triumph in five years.
Kyle Stanley and Spain's Jon Rahm are a further three shots back on six under, six strokes behind Woods.
"Just to be able to compete and play again this year, that's a hell of a comeback", he said.
Woods had never lost when leading by three shots or more going into the final round.
"I just can't believe I pulled this off", added a visibly emotional Woods during the presentation ceremony. Heavy rain left the course playing easy, and Woods was one of the players to take advantage of the conditions. But he was on fire on Saturday, finishing with a 65 and a three-stroke lead for the tournament.
"This whole season has been pretty remarkable considering where I have come from", said Woods.
When holding a lead after 54 holes in his career, it would be quite the understatement to say Woods has been good.
Justin Rose, who entered the day three shots behind Woods, made a key birdie on 18 to win the FedEx Cup title - a four-tournament playoff with a $10 million prize to the victor.
Alzheimer's cases expected to soar in coming decades
The agency report noted that 5 million Americans - 1.6 percent of the population - had Alzheimer's disease in 2014. That number is projected to grow to 13.9 million, almost 3.3 percent of the population, in 2060.
A sea of supporters form a backdrop as Tiger Woods wins his first PGA Tour title since 2013.
The man once associated so intricately with winning won again, in the Tour Championship, by two shots over Billy Horschel, who lent Woods's nerves some late inconvenience.
Rose had said it was a bit more unknown, and "there's a lot on it for him" as well as everyone else.
"I've hit hundreds of millions of putts".
Woods won for the first time in more than five years. Even after shooting an opening-round 62 two weeks ago at the BMW Championship, Woods found himself trailing heading into the weekend, fighting to get in contention.
The 14-time Major victor is a two-time former Tour Championship victor and enjoys a remarkable record of winning 54 of 57 PGA Tour events when holding the 54-hole lead.
The 42-year-old Woods, who returned from an extended absence after spinal fusion surgery in December, has played a comeback season in which his contended several times.