The first recorded usage is attributed to “R. S. Leghorn in H. B. Maynard Top Managem. Handbk. xlvii. 1024,” 1960. He turns out to have been Richard Leghorn, founder of Itek Corporation, which made aerospace spy cameras, and later Chief of Intelligence and Reconnaissance Systems Development at the Pentagon. In a single sentence Leghorn invented the phrase and predicted it would not catch on:

Present and anticipated spectacular informational achievements will usher in public recognition of the “information age,” probably under a more symbolic title.

No better title has come along. Along with information age, the OED now recognizes information storage, information transfer, information processing, information retrieval, information architecture, information superhighway, plus (the bad news) information explosion, gap, warfare, overload, and fatigue.

You don’t need the OED to explain that last one, do you? “Apathy, indifference, or mental exhaustion arising from exposure to too much information …” (Sure enough, even “TMI” has made the dictionary, as a draft addition, colloq.)