There are dozens of answers to this question, since there's evidence that ancient Egypt and Greece had steamboats. Leonardo da Vinci drew plans for steam engines.
In France in 1774, Marquis Claude de Jouffroy and his colleagues had made a 13-metre (42 ft 8 in) working steamboat with rotating paddles, the Palmipède. The ship sailed on the Doubs River in June and July 1776, apparently the first steamship to sail successfully.
In the United States, it was John Fitch or Robert Fulton. Click on each name to read their biographies. Robert Fulton was the first to operate steamboats commercially.
These pages come from the 1856 book, Lloyd's Steamboat Directory and Disasters on the Western Waters, recently reprinted by Jay Richiuso of Land Yacht Press. The Fitch and Fulton biographies are just a portion of the book's introduction. We highly recommend the book - it mainly consists of newspaper articles describing steamboat wrecks, including names of people who died. Great for genealogists.
Click here to see the book at Amazon.com.
There are many theories on who built the first boat before Fitch and Fulton. Believe me, I've heard from the lesser known inventors' descendents and there's a lot of controversy on this subject. In the interest of getting the truth out on the Internet, I have posted every letter I've received on the subject, along with more book titles, and more "first steamboat" theories. Go to the First Boat Blog for more theories and information.
First Boat Blog