Rare, full length circular intron RNAs distinct from lariats have been reported in several species, but their biogenesis is not understood. We envision and test a hypothesis for their formation using Saccharomyces cerevisiae, documenting full length and novel processed circular RNAs from multiple introns. Evidence implicates a previously undescribed catalytic activity of the intron-lariat spliceosome (ILS) in which the 3'-OH of the lariat tail (with optional trimming and adenylation by the nuclear 3' processing machinery) attacks the branch, joining the intron 3' end to the 5' splice site in a 3'-5' linked circle. Human U2 and U12 spliceosomes produce analogous full length and processed circles. Post-splicing catalytic activity of the spliceosome may promote intron transposition during eukaryotic genome evolution.