"It's boyhood dreams", Rose said. "I'm delighted to have got to the top".
There was disappointment too for Rose, whose chip shot came up woefully short, and when his putt agonisingly lipped out, he and Bradley headed back down the 18th.
Bradley, the 2011 PGA Championship victor, captured his fourth PGA Tour title and won for the first time since the WGC-Bridgestone Invitational in 2012. But a No. 1 ranking will do for Rose, who and joins Nick Faldo, Lee Westwood and Luke Donald as the only Englishmen to reach the top spot.
Unlike most tournaments on the PGA Tour, there is a smaller field to split the $9 million prize pool with as the FedEx Cup playoffs have narrowed down the players eligible to compete over the past two weeks.
Tiger Woods is building momentum, putting out his best showing at the 2018 Northern Trust on Saturday with a three-under 68 in the third round.
"When you talk about your career, those are the three highlights (winning a Major, playing in the Ryder Cup and being World No.1)".
The final round was pushed back from Sunday to Monday because of constant rain that led to poor course conditions.
Rose, reigning Olympic champion and 2013 US Open victor, could have sealed victory with a par putt at the last regulation hole but missed narrowly.
Returning for a rare Monday finish due to the weather - for the second week in a row after the traditional Labor Day conclusion to the Deutsche Bank Championship - McIlroy started one shot off Justin Rose.
Woods did make birdie at No. 16 before closing out with a pair of pars.
"If it becomes a situation then, you know, I'll obviously accept whatever fine it is, move on and try and add one new event every year, but it's kind of tough". I thought that thing was in the middle, but it wasn't to be.
Woods took away any suspense about getting back to the Tour Championship for the first time since 2013. Spieth started 27th in the FedEx Cup standings and took a step backward, finishing with a 73 to tie for 55th.
Speaking to Sky Sports about the final FedEx tournament, Rose said: "No 2 is an incredible spot to be in, and it's a week where there are many scenarios in play". "But to get to the end of the season and make it to the Tour Championship, considering what I've been through, is a pretty good accomplishment". He fell out of the top 30 and will miss the Tour Championship for the first time.