New York District Attorney Preet Bharara will present the two books, one of which is 330 years old, over to the library's CEO Gunilla Herdenberg in a ceremony in Manhattan, officials said.
The books, which have an estimated combined value of $100,000, were among at least 56 stolen from the library between 1995 and 2004 by the former head of its manuscript department Anders Burius, who committed suicide shortly after confessing to the thefts in 2004.
The books were sold through Hamburg-based German auction house Ketterer Kunst, with 13 of them going to buyers in the United States.
FBI agents have been trying to track down the missing works and last year succeeded in negotiating the return to Sweden of a 415-year-old atlas that was put up for sale at auction in New York in 2011.
The books that will be returned on Wednesday are a 1683 "Description of Louisiana" by French missionary and explorer Louis Hennepin and a German collection of American artist Henry Lewis's illustrations of Mississippi that was printed in Dusseldorf between 1854-58.
They were bought from Ketterer in the mid-90s by Stephan Loewentheil, an antique book dealer based in Baltimore, Maryland who only learned that the books were stolen when the FBI got in touch with him last year, long after he had sold them.
"Although as a bona fide purchaser, I didn't have any legal liability, from a moral standpoint it bothered me," Loewentheil told AFP.
"So I tracked them down and fortunately the people I had sold them to were willing to sell them back to me, and I repurchased them at my own expense.
"Our clients love books and people who love books tend to want to do the right thing, so they were happy to sell the books back to me.
"All theft is bad, but for me cultural theft is the worst because you are stealing the patrimony of a nation."