According to Wikipedia:

Daniel Hess of West Union, Iowa, USA invented a vacuum cleaner in 1860. Calling it a carpet sweeper instead of a vacuum cleaner, his machine did, in fact, have a rotating brush like a traditional vacuum cleaner, which also possessed an elaborate bellows mechanism on top of the body to generate suction of dust and dirt. Hess received a patent (U.S. No. 29.077) for his invention of the vacuum cleaner on July 10, 1860.