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Document-level machine translation incorporates inter-sentential dependencies into the translation of a source sentence. In this paper, we propose a new framework to model cross-sentence dependencies by training neural machine translation (NMT) to predict both the target translation and surrounding sentences of a source sentence. By enforcing the NMT model to predict source context, we want the model to learn "contextualized" source sentence representations that capture document-level dependencies on the source side. We further propose two different methods to learn and integrate such contextualized sentence embeddings into NMT: a joint training method that jointly trains an NMT model with the source context prediction model and a pre-training & fine-tuning method that pretrains the source context prediction model on a large-scale monolingual document corpus and then fine-tunes it with the NMT model. Experiments on Chinese-English and English-German translation show that both methods can substantially improve the translation quality over a strong document-level Transformer baseline.