A noiseprint is a camera-related artifact that can be extracted from an image to serve as a powerful tool for several forensic tasks. The noiseprint is built with a deep learning data-driven approach that is trained to produce unique noise residuals with clear traces of camera-related artifacts. This data-driven approach results in a complex relationship that governs the noiseprint with the input image, making it challenging to attack. This article proposes a novel neural noiseprint transfer framework for noiseprint-based counter forensics. Given an authentic image and a forged image, the proposed framework synthesizes a newly generated image that is visually imperceptible to the forged image, but its noiseprint is very close to the noiseprint of the authentic one, to make it appear as if it is authentic and thus renders the noiseprint-based forensics ineffective. Based on deep content and noiseprint representations of the forged and authentic images, we implement the proposed framework in two different approaches. The first is an optimization-based approach that synthesizes the generated image by minimizing the difference between its content representation with the content representation of the forged image while, at the same time, minimizing the noiseprint representation difference from the authentic one. The second approach is a noiseprint injection-based approach, which first trains a novel neural noiseprint-injector network that can inject the noiseprint of an image into another one. Then, the trained noiseprint-injector is used to inject the noiseprint from the authentic image into the forged one to produce the generated image. The proposed approaches are generic and do not require training for specific images or camera models. Both approaches are evaluated on several datasets against two common forensic tasks: the forgery localization and camera source identification tasks. In the two tasks, the proposed approaches are able to significantly reduce several forensic accuracy scores compared with two noiseprint-based forensics methods while at the same time producing high-fidelity images. On the DSO-1 dataset, the reduction in the forensic accuracy scores has an average of 75%, while the produced images have an average PSNR of 31.5 dB and SSIM of 0.9. The source code of the proposed approaches is available on GitHub (https://github.com/ahmed-elliethy/nnt).