In this work, we introduce instruction finetuning for Neural Machine Translation (NMT) models, which distills instruction following capabilities from Large Language Models (LLMs) into orders-of-magnitude smaller NMT models. Our instruction-finetuning recipe for NMT models enables customization of translations for a limited but disparate set of translation-specific tasks. We show that NMT models are capable of following multiple instructions simultaneously and demonstrate capabilities of zero-shot composition of instructions. We also show that through instruction finetuning, traditionally disparate tasks such as formality-controlled machine translation, multi-domain adaptation as well as multi-modal translations can be tackled jointly by a single instruction finetuned NMT model, at a performance level comparable to LLMs such as GPT-3.5-Turbo. To the best of our knowledge, our work is among the first to demonstrate the instruction-following capabilities of traditional NMT models, which allows for faster, cheaper and more efficient serving of customized translations.