Well my best guess is it started via a 1970's youth thing in Japan where highschool-age thugs wore 1950's-American style delinquent hair cuts + attitude. But since then, the label has expanded to mean this type of delinquent in general, regardless of whether the specific attributes are American or not. For example, the surgical masks they wear to intimidate people, and they're almost always shown wearing traditional Japanese school uniforms, except "thug-like".
Think Jotaro. He fits the trope to a "T". Space Dandy is also a classic yanki, I can't help thinking that the concept was originally "Space yanki" but changed because of the confusion that term could lead to internationally. there's nothing "dandy" about him, and that's not even a term in Japan for what he is, whereas "yankee" is a real japanese term, which is used to describe people fitting Space Dandy's description, the pompadour haircut, the elvis-type sneer, the way he walks slouched over with his hands in his jacket pockets, all classic Japanese delinquent aka "Yankee."
Warning: tvtropes.
http://tvtropes.org/pmwiki/pmwiki.php/Main/JapaneseDelinquentsFemale delinquents often have their seifuku in some form of purposeful disarray - unknotted scarf, loose socks, partially unbuttoned top, or the skirt hiked up. An unusually long skirt and a coat/jacket also indicates a tough cookie.
In Japanese, delinquents are referred to, both in real life and in fiction, as yankii (as in "yankee", because of their rebelliousness and Hawaiian-patterned shirts they sometimes wore rather than an affinity with the USA), while their leaders are called banchou. Female leaders can be called sukeban or onna banchou.
Fruits Basket, ep1, 5:30 +, other characters call the tall girl a yanki (it's the same in the sub or the dub). elements that make her fit this are, the hair over one eye, mean expression on her face, long skirt (when all other characters in the show have short skirts). extremely long skirts were a popular look for female delinquents in the 1980's. Sometimes they're depicted with a trenchcoat, no shirt and their boobs strapped down with bandages.