This work presents a new search for magnetic monopoles using data taken with the ANTARES neutrino telescope over a period of 10 years (January 2008 to December 2017). Compared to previous ANTARES searches, this analysis uses a run-by-run simulation strategy, with a larger exposure as well as a new simulation of magnetic monopoles taking into account the Kasama, Yang and Goldhaber model for their interaction cross-section with matter. No signal compatible with the passage of relativistic magnetic monopoles is observed, and upper limits on the flux of magnetic monopoles with $\beta$ = v/c $\geq$ 0.55, are presented. For ultra-relativistic magnetic monopoles the flux limit is $\sim$ 7$\times$$10^{-18}$ $\rm cm^{-2} s^{-1} sr^{-1}$. Comment: 20 pages, 7 figures, accepted for publication in the Journal of High Energy Astrophysics