Formal verse poetry imposes strict constraints on the meter and rhyme scheme of poems. Most prior work on generating this type of poetry uses existing poems for supervision, which are difficult to obtain for most languages and poetic forms. In this work, we propose an unsupervised approach to generate poems following any given meter and rhyme scheme, without requiring any poetic text for training. Our method works by splitting a regular, non-poetic corpus into phrases, prepending control codes that describe the length and end rhyme of each phrase, and training a transformer language model in the augmented corpus. During inference, we build control codes for the desired meter and rhyme scheme, and condition our language model on them to generate formal verse poetry. Experiments in Spanish and Basque show that our approach is able to generate valid poems, which are often comparable in quality to those written by humans.