While Neural Machine Translation (NMT) represents the leading approach to Machine Translation (MT), the outputs of NMT models still require translation post-editing to rectify errors and enhance quality, particularly under critical settings. In this work, we formalize the task of translation post-editing with Large Language Models (LLMs) and explore the use of GPT-4 to automatically post-edit NMT outputs across several language pairs. Our results demonstrate that GPT-4 is adept at translation post-editing and produces meaningful edits even when the target language is not English. Notably, we achieve state-of-the-art performance on WMT-22 English-Chinese, English-German, Chinese-English and German-English language pairs using GPT-4 based post-editing, as evaluated by state-of-the-art MT quality metrics.