The stunning victory is worth $11.53 million to former world No. 1 McIlroy, who conjured up a series of magical shots in a thrilling finale to the PGA Tour season.
It was clinched with a birdie putt on the 16th, the fourth hole of the playoff to finally see off the challenge of Moore, with Chappell having dropped out at the first extra hole.
Both Moore and McIlroy parred the next two playoff holes before the Northern Irishman sealed his double triumph.
A win for Moore would have given US Open champion Dustin Johnson the FedEx Cup series and the $10 million bonus on offer at Atlanta's East Lake course.
Johnson, in the joint lead overnight, slipped to a final-round 73 to leave his fate in the hands of others as he tied for sixth and eventually second place in the FedEx standings, and a $3 million prize.
Four-time major champion McIlroy also looked to have fallen short in his last-round challenge until he spectacularly holed his second shot to the 16th for an eagle to move to within one of the lead.
A birdie on the par-five 18th saw the Northern Irishman complete a final round six-under 64 and with both Chappell and Moore only making pars, that left the trio tied on 12-under 268.
The first hole of the playoff on the 18th saw McIlroy stamp his authority with a stunning approach, but after Moore bravely holed his birdie putt, he was left with little over six feet to take the biggest prize in golf -- but it lipped out of the cup.
Chappell, who played so well on the final day in search of his maiden PGA Tour win, could only make par, leaving the way clear for McIlroy and Moore to battle it out in the gathering gloom.
McIlroy had to hole a nerve jangling par putt on the 15th, the third extra hole, to prolong proceedings, before another booming drive on the 16th set up his victory chance.
Moore kept up the pressure when he drained an unlikely par putt from long range, but McIlroy made no mistake with his birdie effort, complete with winning roar.
"I took advantage of my opportunities today and yeah, here we are," McIlroy said, scarcely able to take in his victory.
He will now head to Hazeltine where Europe looks to defend the Ryder Cup against the United States, but clearly on the top of his form after his second win in three tournaments.
Moore will also be there, as the 33-year-old was named in the US Ryder Cup team for the first time
when captain Davis Love made his final wildcard pick after the conclusion of the Tour Championship.