German immigrants introduced the recipe to the US. The term "hamburger" is believed to have appeared in 1834 on the menu from Delmonico's restaurant in New York but there is no surviving recipe for the meal. The first mention in print of "Hamburg steak" was made in 1884 in the Boston Evening Journal.
The honour of producing the first proper hamburger goes to Charlie Nagreen of Seymour, WI. In 1885 Nagreen introduced the American hamburger at the Outgamie County Fair in Seymour. (Seymour is recognized as the hamburger capital of the world.)
However, there is another claim to that throne. There is an account of Frank and Charles Menches who, also in 1885, went to the Hamburg, New York county fair to prepare their famous pork sausage sandwiches. But since the local meat market was out of pork sausage, they used ground beef instead. Alas, another hamburger.
The first account of serving ground meat patties on buns - taking on the look of the hamburger as we know it today - took place in 1904 at the St. Louis World Fair. But it was many years later, in 1921, that an enterprising cook from Wichita, Kansas, Walt Anderson, introduced the concept of the hamburger restaurant. He convinced financier Billy Ingram to invest $700 to create The White Castle hamburger chain. It was an instant success. The rest of the history, we might say, belongs to McDonald's.
And, no, a hamburger does not have any ham in it. Well, it's not supposed to. Hamburger meat usually is made of 70-80% beef, and fat and spices.