In AD&D, there were dual-wielding rules in 1e (1977) but they were not specifically identified with rangers. A high Dexterity did mitigate the associated penalties, however, meaning that characters otherwise concentrating on a high Dexterity, like rangers and rogues, were natural fits for the style. In 2e (1989), rangers got the class ability to avoid the usual -2/-4 dual wielding penalties.
Aragorn, one of the major fictional inspirations for the ranger, did double wield at least once in the Lord of the Rings (at Weathertop), but it wasn't a major part of his deal. Many other historical figures dual wielded including Davy Crockett and other pioneers that commonly fought Indian style with tomahawk and knife, which has some clear ranger analogues. I remember being inspired re: dual wielding by Madmartigan in Willow (1988) but that's too late to drive the 2e rules.
Much of the shift seems to be game mechanic driven. Not being as armored or as hard-hitting as the fighter, the ranger needed something to boost them mechanically, and dual wielding was chosen due to the alignment with high-Dex.
But What About The Drizzle?
Those who weren't around at the time seem to think that this ranger ability stemmed from the fictional exploits of Drizzt Do'Urden in several Forgotten Realms novels. Drizzt the famous double wielding drow ranger was published in 1988 after being made up on the spot in 1987, really too late to affect the course of the 2e rules. Besides, in 1e drow could (debatably in some circles) double wield; his ability to do so is this more about his drow-itude than being a ranger. Not that he was much of a ranger either, his character sheet on wizards.com says Ftr10/Bbn1/Rgr5.
David "Zeb" Cook, designer of 2e, said when asked where the two-weapon ranger came from,
I'm not sure where the ranger took shape, though I know it wasn't an
imposition because of Drizzt. (Frankly, I've never read more than bits
of the Drizzt series.) It was more to make them distinct and it fit
with the style and image.