We introduce Spivavtor, a dataset, and instruction-tuned models for text editing focused on the Ukrainian language. Spivavtor is the Ukrainian-focused adaptation of the English-only CoEdIT model. Similar to CoEdIT, Spivavtor performs text editing tasks by following instructions in Ukrainian. This paper describes the details of the Spivavtor-Instruct dataset and Spivavtor models. We evaluate Spivavtor on a variety of text editing tasks in Ukrainian, such as Grammatical Error Correction (GEC), Text Simplification, Coherence, and Paraphrasing, and demonstrate its superior performance on all of them. We publicly release our best-performing models and data as resources to the community to advance further research in this space.