The $^{19}$F($alpha$,p)$^{22}$Ne reaction is considered to be one of the main sources of fluorine depletion in AGB and Wolf-Rayet stars. The reaction rate still retains large uncertainties due to the lack of experimental studies available. In this work the yields for both exit channels to the ground state and first excited state of $^{22}$Ne have been measured and several previously unobserved resonances have been found in the energy range E$_{lab}$=792-1993 keV. The level parameters have been determined through a detailed R-matrix analysis of the reaction data and a new reaction rate is provided on the basis of the available experimental information.