The pair finished on nine under at a windy Hilton Head before McDowell clinched victory on the first play-off hole after Simpson missed a par putt.
"I played well all week. My putter was cold before I got it going in the final round," said McDowell.
England's Luke Donald finished tied for third on seven under after a 69.
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McDowell also carded a final-round 69 in South Carolina but the Portrush player let slip a one-shot lead when he bogeyed the final hole. Simpson then parred the tough 18th to take the tussle into a play-off.
The players returned to the 18th and McDowell secured his par before Webb bogeyed after missing a 12-foot putt.
McDowell's last victory, in the Valderrama Masters, came in the same year he won the US Open at Pebble Beach.
It is also McDowell's first success on the regular PGA Tour circuit.
"This is one of the premier events on the PGA Tour and it's great to have taken a win on this tour.
"It's a bit special as it's a long time since I won and it feels really nice.
"I played really solidly on Sunday and I holed out well, which was the key to my round.
"I didn't make a ton of putts this week but I didn't make many bogeys, and that's the key to playing well at Hilton Head."
Northern Ireland's Graeme McDowell beat Webb Simpson in a play-off at the RBC Heritage to seal his first win since 2010 and return to the world's top 10.