Context. Magnetohydrodynamic (MHD) waves are ubiquitous in the solar corona where the highly structured magnetic fields provide efficient wave guides for their propagation. While MHD waves have been observed originating from lower layers of the solar atmosphere, recent studies have shown that some can be generated in situ by the collision of dense counter-propagating flows.Aims. In this theoretical study, we analyse the mechanism that triggers the propagation of kink and sausage modes in the solar corona following the collision of counter-propagating flows, and how the properties of the flows affect the properties of the generated waves.Methods. To study in detail this mechanism we ran a series of ideal 2D and 3D MHD simulations where we varied the properties of the counter-propagating flows; by means of a simple technique to estimate the amplitudes of the kink and sausage modes, we investigated their role in the generation and propagation of the MHD waves.Results. We find that the amplitude of the waves is largely dependent on the kinetic energy of the flows, and that the onset of kink or sausage modes depends on the asymmetries between the colliding blobs. Moreover, the initial wavelength of the MHD waves is associated with the magnetic configuration resulting from the collision of the flows. We also find that genuine 3D systems respond with smaller wave amplitudes.Conclusions. In this study, we present a parameter space description of the mechanism that leads to the generation of MHD waves from the collision of flows in the corona. Future observations of these waves can be used to understand the properties of the plasma and magnetic field of the solar corona.