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 semi-analytical framework to model this scenario, and find that the the comoving merger rate of SMBH-IMBH binaries is ∼ 10 −3 Gpc −3 yr −1 in the local Universe for a unity IMBH occupation fraction, scales linearly with it, and has a peak at z ≈ 0.5-3. Our model predicts ∼ 1 event yr −1 within redshift z ≈ 3.5 if 10% of the inspiralled star clusters hosted an IMBH, while ∼ 10 events 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.1. INTRODUCTION The formation and evolution of the innermost galactic regions is still uncertain. Most of the observed galactic nuclei harbour supermassive black holes (SMBHs), with masses ∼ 10 5 -10 9 (e.g., Ferrarese & Merritt 2000; Kormendy & Ho 2013). Galaxies across the entire Hubble sequence also show the presence of nucleated central regions, the nuclear star clusters (NSCs). NSCs are generally very massive, with mass up to a few times 10 7 M , and very dense, with half-light radius of a few pc (e.g., Georgiev et al. 2016;Neumayer et al. 2020). In some galaxies, as our own Milky Way, SMBHs and NSCs are found to co-exist (e.g., Capuzzo-Dolcetta & Tosta e Melo 2017).NSCs typically contain a predominant old stellar population, with age 1 Gyr, and show also the presence of a young stellar population, with age 100 Myr (e.g.,