Tyrosyl-DNA phosphodiesterase I (Tdp1) is a DNA repair enzyme conserved across eukaryotes that catalyzes the hydrolysis of the phosphodiester bond between the tyrosine residue of topoisomerase I and the 3′-phosphate of DNA. Atomic level details of the mechanism of Tdp1 are proposed and analyzed using a fully quantum mechanical, geometrically constrained model. The structural basis for the computational model is the vanadate-inhibited crystal structure of human Tdp1 (hTdp1, Protein Data Bank entry 1RFF). Density functional theory computations are used to acquire thermodynamic and kinetic data along the catalytic pathway, including the phosphoryl transfer and subsequent hydrolysis. Located transition states and intermediates along the reaction coordinate suggest an associative phosphoryl transfer mechanism with five-coordinate phosphorane intermediates. Similar to both theoretical and experimental results for phospholipase D, the proposed mechanism for hTdp1 also includes the thermodynamically favorable possibility of a four-coordinate phosphohistidine “dead-end” product.