We present RECAP (REtrieval-Augmented Audio CAPtioning), a novel and effective audio captioning system that generates captions conditioned on an input audio and other captions similar to the audio retrieved from a datastore. Additionally, our proposed method can transfer to any domain without the need for any additional fine-tuning. To generate a caption for an audio sample, we leverage an audio-text model CLAP to retrieve captions similar to it from a replaceable datastore, which are then used to construct a prompt. Next, we feed this prompt to a GPT-2 decoder and introduce cross-attention layers between the CLAP encoder and GPT-2 to condition the audio for caption generation. Experiments on two benchmark datasets, Clotho and AudioCaps, show that RECAP achieves competitive performance in in-domain settings and significant improvements in out-of-domain settings. Additionally, due to its capability to exploit a large text-captions-only datastore in a \textit{training-free} fashion, RECAP shows unique capabilities of captioning novel audio events never seen during training and compositional audios with multiple events. To promote research in this space, we also release 150,000+ new weakly labeled captions for AudioSet, AudioCaps, and Clotho.