Gravitational waves (GWs) offer an unprecedented opportunity to survey the sky and detect mergers of compact objects. While intermediate-mass black holes (IMBHs) have not been detected beyond any reasonable doubt with either dynamical or accretion signatures, the GW landscape appears very promising. Mergers of an IMBH with a supermassive black hole (SMBH) will be primary sources for the planned space-based mission LISA and could be observed up to the distant universe. SMBH–IMBH binaries can be formed as a result of the migration and merger of stellar clusters at the center of galaxies, where an SMBH lurks. We build for the first time a semianalytical framework to model this scenario and find that the comoving merger rate of SMBH–IMBH binaries is ∼10−4 Gpc−3 yr−1 in the local universe for a unity IMBH occupation fraction, scales linearly with it, and has a peak at z ≈ 0.5–2. Our model predicts ∼0.1 events yr−1 within redshift z ≈ 3.5 if 10% of the inspiraled star clusters hosted an IMBH, while ∼1 event yr−1 for a unity occupation fraction. More than 90% of these systems will be detectable with LISA with a signal-to-noise ratio larger than 10, promising to potentially find a family of IMBHs.