•Ultrashort acoustic pulses excite exchange magnons in ferromagnetic thin films.•Excitation efficiently is determined by acoustic bandwidth.•Analytical theory of magnon excitation py ultrashort acoustic pulses is given.•Magnon excitation follows the equation of a driven harmonic oscillator.•Numerical simulations for thin nickel films are presented. We investigate generation of exchange magnons by ultrashort, picosecond acoustic pulses propagating through ferromagnetic thin films. Using the Landau-Lifshitz-Gilbert equations we derive the dispersion relation for exchange magnons for an external magnetic field tilted with respect to the film normal. Decomposing the solution in a series of standing spin wave modes, we derive a system of ordinary differential equations and driven harmonic oscillator equations describing the dynamics of individual magnon mode. The external magnetoelastic driving force is given by the time-dependent spatial Fourier components of acoustic strain pulses inside the layer. Dependencies of the magnon excitation efficiencies on the duration of the acoustic pulses and the external magnetic field highlight the role of acoustic bandwidth and phonon-magnon phase matching. Our simulations for ferromagnetic nickel evidence the possibility of ultrafast magneto-acoustic excitation of exchange magnons within the bandwidth of acoustic pulses in thin samples under conditions readily obtained in femtosecond pump-probe experiments.