Far-ultraviolet (FUV) scintillation signals have been measured in heavy noble gases (argon, krypton, xenon) following boron-neutron capture ($^{10}$B($n,alpha$)$^7$Li) in $^{10}$B thin films. The observed scintillation yields are comparable to the yields from some liquid and solid neutron scintillators. At noble gas pressures of 107 kPa, the number of photons produced per neutron absorbed following irradiation of a 1200 nm thick $^{10}$B film was 14,000 for xenon, 11,000 for krypton, and 6000 for argon. The absolute scintillation yields from the experimental configuration were calculated using data from (1) experimental irradiations, (2) thin-film characterizations, (3) photomultiplier tube calibrations, and (4) photon collection modeling. Both the boron films and the photomultiplier tube were characterized at the National Institute of Standards and Technology. Monte Carlo modeling of the reaction cell provided estimates of the photon collection efficiency and the transport behavior of $^{10}$B($n,alpha$)$^7$Li reaction products escaping the thin films. Scintillation yields increased with gas pressure due to increased ionization and excitation densities of the gases from the $^{10}$B($n,alpha$)$^7$Li reaction products, increased frequency of three-body, excimer-forming collisions, and reduced photon emission volumes (i.e., larger solid angle) at higher pressures. Yields decreased for thicker $^{10}$B thin films due to higher average energy loss of the $^{10}$B($n,alpha$)$^7$Li reaction products escaping the films. The relative standard uncertainties in the measurements were determined to lie between 14 % and 16 %. The observed scintillation signal demonstrates that noble gas excimer scintillation is promising for use in practical neutron detectors.