Verb, transitive, from the brand of vacuum cleaner, which was apparently hugely popular in the U.K in the mid-20th-century period. The OED reports that the literal verb–that is, to clean by means of a vacum cleaner–appeared no later than 1939 (impressive, since Hoover was patented only in 1927). The first cite for the metaphorical verb (“To consume voraciously; to devour completely. Freq. with up or (occas.) in”) is from the 1970 Times: “The populace‥sit hoovering up the drivel poured out on television at peak viewing times.” A Google Ngram suggests that, as with so many Britishisms, U.S. use started to rise in the early 90s and is still going up.
Urban Dictionary offers two additional meanings for the verb. One of them you can guess. The other:
Being manipulated back into a relationship against your will with threats of suicide or self-harm, threats of harm to others or property, or threats of false criminal accusations. A “hoover” is relationship blackmail. This slang term is often associated with individuals suffering from personality disorders like Borderline Personality Disorder or Narcissistic Personality Disorder.
“Where are we rolling?” “Into the heart of the night. Wherever there are dances to be danced, drugs to be hoovered.” (Jay McInerney, Bright Lights, Big City, 1984)/For years, Mr. Madoff’s elusive genius act beguiled his Jewish neighbors, as well as friends of those neighbors, and so on, and so on, until vast chunks of local money were hoovered into his Ponzi scheme. (New York Times, April 11, 2009)
notoneoffbritishisms.com 
As well as being a verb “I’m going to hoover the floor” it’s also a generic term for a vacuum cleaner here “I’m going out to buy a new hoover”, which may or may not be of the Hoover brand.
I was astonished to hear a wholly American NPR reporter gratuitously employing this Britishism this morning when referring to the controversy about the National Security Agency monitoring e-mails and phone records, as in “The U.S. is accused of hoovering up huge amounts of private information at home and abroad for what it says is an effort to find terrorists.” I’m familiar with the term, but it’s a particularly obnoxious one to be used by someone with no apparent connection with the United Kingdom.
John, nothing to do with J Edgar, I suppose!
Common tendency on both sides of the pond. Brits: biro (invisible in AmE since 1900), sellotape; Americans: saran wrap, scotch tape, band-aid, jello, sharpie. And surely many others
I’m a little astonished to learn that “hoover” as a verb is originally a Britishism. In the States, I’ve been hearing it in this context fairly often for most of my life (i.e. at least 35-40 years), from coast to coast. Certainly not contesting where it originated, but it’s pretty darn entrenched in American English at this point. I haven’t seen this site before, not sure about the “typical visitor” demographic, if there is one. But with the vote tally on this one reporting ~56% saying it’s “over the top” that Americans would use this word in this way — wow! It’s been a very long time, folks.
And anyway… isn’t imitation the sincerest form of flattery?