And he will face a possible penalty from the PGA Tour for failing to play enough events this year as part of its field enhancement criteria.
Spieth began the year ranked second in the world but has dropped to 10th after failing to win and posting just five top-10 finishes.
"I didn't think that it mattered much but I knew if I could shoot 4-, 5-under in tough conditions that it would make a little bit of a difference, " Spieth said.
How exactly do you process missing a short par putt for victory at a major FedEx Cup event and going on to lose to Keegan Bradley in a play-off, but still being crowned the new World No 1 for the first time in your career?
The final round had been scheduled for Sunday but was postponed until Monday after persistent rain made the Aronimink course unplayable.
Bradley shot a final round 6-under 64 to finish at 20-under par, tied with Rose, who lipped out with his potentially winning putt, which was just so close.
Americans Billy Horschel and Xander Schauffele shared third on 261 with Northern Ireland s Rory McIlroy on 262.
Speaking about his new ranking, he added: "That's obviously boyhood dream stuff, something I'm incredibly proud of".
"No 2 is an incredible spot to be in, and it's a week where there are many scenarios in play", he said. "It's over before you know it", Rose said. The top 30 on a season-long points list advance to next week's Tour Championship in Atlanta.
Mathematically, Woods still has a chance to win the FedEx Cup, although it would require several top players to lose form.
Organisers confirmed that Casey pulled out of the weather-delayed event due to a back problem shortly ahead of the resumption of play on Monday morning.
Players are required to play in 25 events in a season or risk a fine; Spieth played in 24 events and was clearly banking on making East Lake his 25th.
"I was in control of my own destiny and didn't have it this week", he added.