Monday's victory marks the end of a six-year slump for Bradley, the 2011 PGA champion, who dipped as low as 122nd in the world in 2016.
"That's an awesome achievement, something I'm extraordinarily proud of", the Englishman said in a greenside interview after becoming the 22nd man to hold the top spot since the rankings began in 1986.
Bradley, who fired a six-under 64 in the final round after beginning the day three shots behind Rose, had been watching anxiously at the side of the course with his family and he then returned to take advantage of his extra opportunity. "I was just trying to play".
After being tied for the lead with an opening-round 62 on Thursday, Woods shot 70 and 66 over the next two days to put himself behind a deep pack of players atop the leaderboard. "It's tough to go from being on Ryder Cup teams, being on Presidents Cup teams to being outside the top 100 in the world".
Keegan Bradley held off Justin Rose to win the BMW Championship in a playoff. But [I'm] delighted to have got to the top.' Rose looked on course for the tenth PGA Tour title of his career after Bradley bogeyed the 18th.
"I've played a few tournaments where I've come close at the end, and just didn't quite, obviously, get the 'W, '" Woods said. His swing was worthy of a multi-shot win but he again missed key birdie chances throughout the week. Bradley finished sixth in Strokes Gained: Putting this week.
By getting into the Tour Championship, Woods also earns a spot in next year's WGC-Mexico Championship.
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Luck took off running, was an automatic challenge for Cincinnati's defenders since he can slide and give himself up at any point. The Colts quarterback was rushing to get a first down on third and seven and dove for the marker in the middle of the field.
The plan is for groups of three to begin play at 7:30 am EST off two tees at a time. That was about the time he was just starting to cope with back pain.
"To say that I made it back to the Tour Championship after what I've been through is a pretty good accomplishment", Woods said.
As Bradley thrust his arms into the air, his family joined him in celebration on the green. Spieth started 27th in the FedEx Cup standings and took a step backward, finishing with a 73 to tie for 55th.
Even though Woods prefers tougher conditions this is the second time over the last month he's almost gotten it done in a birdie-fest, including the PGA Championship at Bellerive.
Still to be determined is the penalty.
The top 30 on a season-long points list advance to the Tour Championship in Atlanta starting on Thursday week. Not that he played poorly, more that his reward would have been greater had it ended after three rounds.
"I assume it will either be a fine or I'm adding some [events] in the fall".