Automatic artistic text generation is an emerging topic which receives increasing attention due to its wide applications. The artistic text can be divided into three components, content, font, and texture, respectively. Existing artistic text generation models usually focus on manipulating one aspect of the above components, which is a sub-optimal solution for controllable general artistic text generation. To remedy this issue, we propose a novel approach, namely GenText, to achieve general artistic text style transfer by separably migrating the font and texture styles from the different source images to the target images in an unsupervised manner. Specifically, our current work incorporates three different stages, stylization, destylization, and font transfer, respectively, into a unified platform with a single powerful encoder network and two separate style generator networks, one for font transfer, the other for stylization and destylization. The destylization stage first extracts the font style of the font reference image, then the font transfer stage generates the target content with the desired font style. Finally, the stylization stage renders the resulted font image with respect to the texture style in the reference image. Moreover, considering the difficult data acquisition of paired artistic text images, our model is designed under the unsupervised setting, where all stages can be effectively optimized from unpaired data. Qualitative and quantitative results are performed on artistic text benchmarks, which demonstrate the superior performance of our proposed model. The code with models will become publicly available in the future.