Harry,
Researchers have been tossing this one around for quite some time. The accepted answer is that Funnies on Parade, which was released as a give-away in 1933 is the first comic book in the modern format. Famous Funnies #1 was the first comic book that was sold and it was released in 1934. Both books featured reprints of popular comic strips. The first comic to feature original characters was New Fun Comics #1 released in 1935 and it was also the first comic from DC.
Some want to quibble about what makes a comic book and even date the first comics back to the late 1800s, however, I tend to stick with the stock answer, since the comics I have listed above are in the format that we have come to accept as a comic book.

Comics Q & A with Snugs Baxter