In recent years, deep Convolutional Neural Networks (CNNs) have broken all records in salient object detection. However, training such a deep model requires a large amount of manual annotations. Our goal is to overcome this limitation by automatically converting an existing deep contour detection model into a salient object detection model without using any manual salient object masks. For this purpose, we have created a deep network architecture, namely Contour-to-Saliency Network (C2S-Net), by grafting a new branch onto a well-trained contour detection network. Therefore, our C2S-Net has two branches for performing two different tasks: (1) predicting contours with the original contour branch, and (2) estimating per-pixel saliency score of each image with the newly-added saliency branch. To bridge the gap between these two tasks, we further propose a contour-to-saliency transferring method to automatically generate salient object masks which can be used to train the saliency branch from outputs of the contour branch. Finally, we introduce a novel alternating training pipeline to gradually update the network parameters. In this scheme, the contour branch generates saliency masks for training the saliency branch, while the saliency branch, in turn, feeds back saliency knowledge in the form of saliency-aware contour labels, for fine-tuning the contour branch. The proposed method achieves state-of-the-art performance on five well-known benchmarks, outperforming existing fully supervised methods while also maintaining high efficiency.