Injection seeding of solid-target soft x-ray laser amplifiers with high harmonic pulses is shown to dramatically improve the far-field laser beam profile and reduce the beam divergence. Measurements and two-dimensional simulations for a 13.9 nm nickel-like Ag amplifier show that the amplified beam divergence depends strongly on the seed and can therefore be controlled by selecting the divergence of the seed. The near-field beam size of both the seeded and unseeded lasers is shown to be determined by the size of the gain region and the divergence of the amplified beams.