A measurement of the $\Xi_{cc}^{++}$ mass is performed using data collected by the LHCb experiment between 2016 and 2018 in $pp$ collisions at a centre-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 5.6 $\mathrm{fb}^{-1}$. The $\Xi_{cc}^{++}$ candidates are reconstructed via the decay modes $\Xi_{cc}^{++}\to\Lambda_c^+K^-\pi^+\pi^+$ and $\Xi_{cc}^{++}\to\Xi_c^+\pi^+$. The result, $3621.55 \pm 0.23{\rm,(stat),} \pm 0.30 {\rm,(syst),}{\rm MeV}/c^2$, is the most precise measurement of the $\Xi_{cc}^{++}$ mass to date.