We present MLQE-PE, a new dataset for Machine Translation (MT) Quality Estimation (QE) and Automatic Post-Editing (APE). The dataset contains annotations for eleven language pairs, including both high- and low-resource languages. Specifically, it is annotated for translation quality with human labels for up to 10,000 translations per language pair in the following formats: sentence-level direct assessments and post-editing effort, and word-level binary good/bad labels. Apart from the quality-related scores, each source-translation sentence pair is accompanied by the corresponding post-edited sentence, as well as titles of the articles where the sentences were extracted from, and information on the neural MT models used to translate the text. We provide a thorough description of the data collection and annotation process as well as an analysis of the annotation distribution for each language pair. We also report the performance of baseline systems trained on the MLQE-PE dataset. The dataset is freely available and has already been used for several WMT shared tasks.