Puzo's novels spawned the critically-acclaimed films directed by Francis Ford Coppola and starring veteran actors Robert De Niro, Al Pacino and Marlon Brando.
Paramount sued Puzo's estate three months ago, in a bid to stop the publication of an unauthorised prequel to the Godfather saga titled The Family Corleone, written by Ed Falco and based on a screenplay by the late Puzo.
Deadline now reports that Puzo's son Anthony Puzo has agreed to put all profits for the book in escrow until the publishing rights are cleared up.
The book was released earlier this week.
Paramount attorney Richard Kendall has said that his clients are satisfied with the new deal, although things may become more complicated if "there's an attraction to do a movie".
It is unclear whether director Francis Ford Coppola would be involved in any future projects regarding the series. He recently went on record to say that there should have never been any sequels to the first Godfather movie.