Kelley vouches for the truth in "The Family: The Real Story of the Bush Dynasty," published Tuesday, the Washington Post reported.
"This book has been vetted by four sets of lawyers, including the chief counsel of Random House," Kelley told morning show host Matt Lauer Monday on the "Today" show.
The allegations reportedly came from Sharon Bush, ex-wife of the president's brother, Neil, although the former sister-in-law has adamantly denied making the claims.
When Lauer asked Kelley why she didn't tape the Sharon Bush interview, which reportedly took place in a New York restaurant, the author said ambient noise would have interfered with the recording, so she didn't bother.
Later on Monday's "Today" show, Sharon Bush repeated her denial of telling Kelley about Bush's drug use, saying she was stunned the author attributed the information to her.