Introns are a fundamental component of eukaryotic genome architecture with poorly understood origins. Recently, we proposed that intron generating transposable elements, introners, are the major driver of intron gain in diverse eukaryotic lineages. However, the molecular mechanism(s) and population processes of introner propagation remain elusive and the means of spread into new lineages is largely unknown. We analyze 8719 genomes, revealing 1695 novel intron generating TEs in 693 species spanning nearly every represented eukaryotic lineage. Introners contain functional protein domains and sequence features consistent with diverse TEs including canonical terminal-inverted-repeat DNA TEs, long terminal repeat retrotransposons and tyrosine recombinases as well as a myriad of novel TEs with uncharacterized molecular mechanisms. We identify several cases where introners have recently horizontally transferred between highly genetically divergent host species. Our results indicate that intron gain is an almost inevitable consequence of transposable element activity and transfer among eukaryotic lineages thereby resolving a central mystery of genome structure evolution.