Recent approaches to the Automatic Post-editing (APE) of Machine Translation (MT) have shown that best results are obtained by neural multi-source models that correct the raw MT output by also considering information from the corresponding source sentence. To this aim, we present for the first time a neural multi-source APE model based on the Transformer architecture. Moreover, we employ sequence-level loss functions in order to avoid exposure bias during training and to be consistent with the automatic evaluation metrics used for the task. These are the main features of our submissions to the WMT 2018 APE shared task, where we participated both in the PBSMT subtask (i.e. the correction of MT outputs from a phrase-based system) and in the NMT subtask (i.e. the correction of neural outputs). In the first subtask, our system improves over the baseline up to -5.3 TER and +8.23 BLEU points ranking second out of 11 submitted runs. In the second one, characterized by the higher quality of the initial translations, we report lower but statistically significant gains (up to -0.38 TER and +0.8 BLEU), ranking first out of 10 submissions.