Using a first-principles approach, we calculate core-level shifts at the Si(001)-SiO₂ interface. By fully relaxing interfaces between Si and tridymite, a crystalline form of SiO₂, we obtain interface models with good local structural properties and with no electronic states in the Si gap. Calculated values of Si 2p core-level shifts agree well with data from photoemission experiments and show a linear dependence on the number of nearest-neighbor oxygen atoms. Core-hole relaxation accounts for ∼50% of the total shifts, in good agreement with Auger experiments.