Short (15-30 residue) chains of amino acids at the amino termini of expressed proteins known as signal peptides (SPs) specify secretion in living cells. We trained an attention-based neural network, the Transformer model, on data from all available organisms in Swiss-Prot to generate SP sequences. Experimental testing demonstrates that the model-generated SPs are functional: when appended to enzymes expressed in an industrial Bacillus subtilis strain, the SPs lead to secreted activity that is competitive with industrially used SPs. Additionally, the model-generated SPs are diverse in sequence, sharing as little as 58% sequence identity to the closest known native signal peptide and 73% ± 9% on average.