Binary interaction can cause stellar envelopes to be stripped, which significantly reduces the radius of the star. The orbit of a binary composed of a stripped star and a compact object can therefore be so tight that the gravitational radiation the system produces reaches frequencies accessible to the Laser Interferometer Space Antenna (LISA). Two such stripped stars in tight orbits with white dwarfs are known so far (ZTF J2130+4420 and CD−30°11223), but many more are expected to exist. These binaries provide important constraints for binary evolution models and may be used as LISA verification sources. We develop a Monte Carlo code that uses detailed evolutionary models to simulate the Galactic population of stripped stars in tight orbits with either neutron star or white dwarf companions. We predict 0–100 stripped star + white dwarf binaries and 0–4 stripped star + neutron star binaries with a signal-to-noise ratio >5 after 10 yr of observations with LISA. More than 90% of these binaries are expected to show large radial velocity shifts of \(\gtrsim\)200 km s-1, which are spectroscopically detectable. Photometric variability due to tidal deformation of the stripped star is also expected and has been observed in ZTF J2130+4420 and CD−30°11223. In addition, the stripped star + neutron star binaries are expected to be X-ray bright with LX \(\gtrsim\) 1033–1036 erg s-1. Our results show that stripped star binaries are promising multimessenger sources for the upcoming electromagnetic and gravitational wave facilities. We provide detailed information about the run presented in Figures 2, 4, and 5 in the file named "entire_population_64.txt". We also provide information about sources with SNR > 4 in "pop_SNR4.txt" for 1000 runs of our standard model. The Jupyter notebook "Reading_stripped_star_compact_object_population.ipynb" reproduces figures of the manuscript and the Jupyter notebook "living_population.ipynb" shows how we model the Galactic population of stripped stars in tight orbit with compact objects.