The arrests were made late on Wednesday night in two different places around the town of Beccles in Suffolk.
Police are to question the 16 year olds, as well as a 44-year-old man from the Beccles area, and an 18-year-old man from Norfolk later on Thursday.
JK Rowling is taking action
They have been officially arrested in connection with the theft of the books from a printing company in Bungay, and on suspicion of "obtaining property by deception".
The top secret fifth Potter books were found in a field by a man out walking on Tuesday.