The diversification of gene functions has been largely attributed to the process of gene duplication. Novel examples of genes originating from previously untranscribed regions have been recently described without regard to a unifying functional mechanism for their emergence. Here we propose a model mechanism that could generate a large number of lineage-specific novel transcripts in vertebrates through the activation of bidirectional transcription from unidirectional promoters. We examined this model in silico using human transcriptomic and genomic data and identified evidence consistent with the emergence of more than 1,000 primate-specific transcripts. These are transcripts with low coding potential and virtually no functional annotation. They initiate at less than 1 kb upstream of an oppositely transcribed conserved protein coding gene, in agreement with the generally accepted definition of bidirectional promoters. We found that the genomic regions upstream of ancestral promoters, where the novel transcripts in our dataset reside, are characterized by preferential accumulation of transposable elements. This enhances the sequence diversity of regions located upstream of ancestral promoters, further highlighting their evolutionary importance for the emergence of transcriptional novelties. By applying a newly developed test for positive selection to transposable element-derived fragments in our set of novel transcripts, we found evidence of adaptive evolution in the human lineage in nearly 3% of the novel transcripts in our dataset. These findings indicate that at least some novel transcripts could become functionally relevant, and thus highlight the evolutionary importance of promoters, through their capacity for bidirectional transcription, for the emergence of novel genes.