We have produced a large set of broadband (0–10 Hz) synthetic seismograms for Mw 9.0 earthquakes on the Cascadia megathrust by combining synthetic seismograms derived from 3D finite‐difference simulations (⁠≤1  Hz⁠) with finite‐source, stochastic synthetics (⁠≥1  Hz⁠). We used a compound rupture model consisting of high stress drop M_w 8 subevents superimposed on large, shallower slip with long‐slip duration, informed by observations of the M_w 9.0 Tohoku, Japan, and M_w 8.8 Maule, Chile, earthquakes. Thirty 3D simulations were run, considering a variety of rupture parameters, to determine the range of expected ground motions. For sites not in sedimentary basins, the spectral accelerations of the synthetics are similar to the BC Hydro ground‐motion prediction equations (GMPEs) for periods of 0.1–6 s, but exceed them at periods greater than 6 s. Response spectra from the synthetics at sites in the Seattle and Tacoma sedimentary basins show large amplifications of factors of 2–5 at periods of 1–10 s. This basin amplification is substantially larger than that found for crustal earthquakes in the Next Generation Attenuation‐West2 (NGA‐West2) GMPEs. Basin amplification is caused by basin‐edge generated surface waves and by amplification and focusing of S waves and surface waves by the 3D basin structure. The synthetic seismograms show effective average durations of strong motions of about 70 s for coastal sites, increasing to about 120 s at 200 km distance. We find that the interevent and intraevent standard deviations of the spectral amplitudes of the synthetics are larger for sites closer to the rupture, because they are more sensitive to the location of subevents and rupture directivity.