OED defines cheeky as “insolent or audacious in address; coolly impudent or presuming” and cites a first appearance in 1859. It was not unknown in the U.S. in subsequent years; a New York Times headline from 1885 read, HOW HILL HELPED PATRICK.; A CHEEKY CIRCULAR SENT THROUGH CHEMUNG COUNTY BY PONY EXPRESS. In 1943, the American writer Max Shulman published a comic novel with the amusing title “Barefoot Boy with Cheek.”
But the Google Ngram below shows that, as with many Britishisms, American only increased significantly in the 1980s.
Presumably, its popularity was helped along by Mike Myers’ late-80s Saturday Night Live character Simon, one of whose catchphrases was “Cheeky monkey!”
Years after retiring, she became friendly with a 37-year-old cheeky chap who had the habit of forging her name on big checks. (New York Times, March 4, 1990). My man Mark Thompson puts up a cheeky post yesterday that I most heartily approved of. (Thomas P.M Barnett, Time.com, August 9, 2011)