In 1817 American papermaker Thomas Gilpin set up the first papermaking machine in America at his mill near Philadelphia. Gilpin obtained the U.S. patent for the first continuous papermaking machine in the U.S., based on information secured by his brother in England. According to Dard Hunter, the machine, which was based on the Dickinson cylinder-mould principle, did the work of ten vats in the handmade mills.
The first newspaper to use Gilpin's machine-made paper was was Poulson's American Daily Advertiser published in Philadelphia on April 15, 1818. Probably the first American book printed on American machine-made paper was Mathew Carey's General Atlas, Improved and Enlarged (Philadelphia: M. Carey & Son, 1818).
The first American book to advertise that it was printed on Gilpin's machine made paper was Carey's edition of Lavoisne's A Complete Geneological, Historical, Chronological and Geograpical Atlas (1820). At the foot of its title page the book indicated that it was "Published by M. Carey and Sons and printed by T. H. Palmer on the Ruthven Press, and on J. & T. Gilpin's Machine Paper."
Hunter, Papermaking: The History and Technique of an Ancient Craft (1947) 538.
Thanks to John Bidwell, who informed me by email in January 2015 that Carey's 1818 book was the earliest American book that he had seen printed on American machine-made paper.