A Random House spokesperson told The New York Times on Monday (October 8) that a deal had been reached with Dunham, but declined to confirm rumours of a multimillion dollar contract.
Susan Kamil, editor-in-Chief of Random House, said of the acquisition: "We're thrilled to welcome Lena to Random House. Her skill on the page as a writer is remarkable - fresh, wise, so assured.
"She is that rare literary talent that will only grow from strength to strength and we look forward to helping her build a long career as an author."
Dunham's book is to be titled Not That Kind of Girl: A Young Woman Tells You What She's Learned, a modern take on the work of Helen Gurley Brown.
The actress-writer said on Monday that she is "thrilled to be" collaborating with the publishing house's "brilliant minds".
"I look forward to digging deep with Andy and co. to produce the most thoughtful and personal book I can," Dunham commented.
Dunham was reportedly offered millions by publishers to secure rights for the project during meetings held on Friday.
The second series of the Emmy-nominated Girls is to premiere in January 2013 on HBO.
Watch a trailer for Girls season one below: