The book, due to be released in September, has the Swedish title "The Man who Chased his Shadow" (Mannen som sökte sin skugga). Like all of the other books in the series, Salander will be the main character.
She will begin the novel serving a short sentence at a women's prison, where she is attempting to avoid conflicts between prisoners, and the tale will develop into a story of "state abuse, honour problems and shadows from a childhood that still haunts Salander".
The cover of the new book. Photo: Norstedts
Lagercrantz wrote the fourth book in the series, The Girl in the Spider's Web, which was published in 2015. He followed on from original author Stieg Larsson, who died of a heart attack in 2004 before the first trilogy became an international smash hit, spawning movie adaptations and even a Hollywood blockbuster version of the first in the series, The Girl with the Dragon Tattoo.
Continuing the series without Larsson was a controversial move, leading to childhood friends of the author criticizing the Swedish legal system for not protecting his work. Larsson's longtime partner Eva Gabrielsson also vehemently opposed the move.
"They say heroes are supposed to live forever. That's a load of crap, this is about money,” Gabrielsson said in 2015.
In an interview with Swedish newspaper Dagens Nyheter coinciding with the announcement that he has finished the fifth book, Lagercrantz said he has "to remain faithful to the universe created by Stieg Larsson".
"The task of writing these books is an enormous responsibility, especially since the pressure from abroad is so huge. My job is to find a plot that will continue to make sense. In the end I have," he added.
The Girl in the Spider's Web has sold six million copies since its 2015 release. Lagercrantz is also due to write the sixth book and complete the second trilogy in the series before moving on to a new project.