Ignition delays of lean dimethyl ether (DME)/hydrogen mixtures with hydrogen mole fraction ranging from 0 to 85% were measured using a rapid compression machine with equivalence ratios from 0.3 to 0.5, temperatures from 621 to 852 K and pressures from 7 to 22 bar. Numerical analysis was performed based on the NUI Aramco Mech 2.0 and, in general, good agreement between measurements and predictions was demonstrated. Both measurements and predictions show that H-2 addition increases the ignition delay of DME/H-2 mixtures nonlinearly. Moreover, the effect of H-2 addition on ignition delay becomes more pronounced at H-2 mole fraction above 70% and lower pressure. The dilution and chemical effects of H-2 addition were quantified, and the dilution effect decreases whereas the chemical effect increases with the increase of H-2 mole fraction. It is also found that DME/H-2 mixtures show a three-stage heat release behavior at very lean condition (phi = 0.3), namely, a low temperature heat release (LTHR) stage followed by two high temperature heat release (HTHR) stages. The first- and second-stage HTHR are caused by the conversion of HCHO to CO and the production of final reaction products CO2 and H2O respectively. Overall, DME is mainly consumed during the LTHR and first-stage HTHR whereas H-2 is mainly consumed during the second-stage HTHR. The two-stage HTHR behavior of DME/H-2 mixtures occurs when H-2 and HCHO produced during DME's LTHR stage are present in a proper proportion prior to high-temperature ignition and the temperature after LTHR has reached a proper level.