The English title of the new book is "The Girl Who Takes an Eye for an Eye" and it was released here in Sweden on Thursday. It will roll out worldwide in the coming days.
Lagercrantz also wrote a stand-alone fourth book in the series after the series' originator, Stieg Larsson, passed away in 2004.
Lagercrantz said writing the fifth book was more enjoyable the second time around.
"I was scared to death when I wrote my first, the fourth, book in the series," he told Radio Sweden. This time, however, "was different, it was more fun, I was braver."
The fourth book was published in 47 countries and six million copies have been sold, according to publisher Norstedt's website.