Ribonuclease P (RNase P) is an essential enzyme that processes the 5' leader sequence of precursor tRNA. Eubacterial RNase P is an RNA enzyme, while its eukaryotic counterpart acts as catalytic ribonucleoprotein, consisting of RNA and numerous protein subunits. To study the latter form, we reconstitute human RNase P activity, demonstrating that the subunits H1 RNA, Rpp21, and Rpp29 are sufficient for 5' cleavage of precursor tRNA. The reconstituted RNase P precisely delineates its cleavage sites in various substrates and hydrolyzes the phosphodiester bond. Rpp21 and Rpp29 facilitate catalysis by H1 RNA, which seems to require a phylogenetically conserved pseudoknot structure for function. Unexpectedly, Rpp29 forms a catalytic complex with M1 RNA of E. coli RNase P. The results uncover the core components of eukaryotic RNase P, reveal its evolutionary origin in translation, and provide a paradigm for studying RNA-based catalysis by other nuclear and nucleolar ribonucleoprotein enzymes.