In linac-driven free-electron lasers, colliders, and energy recovery linacs, a common way to compress the electron bunch to kiloampere level is based upon the implementation of a magnetic dispersive element that converts particle energy deviation into a path-length difference. Nonlinearities of such a process are usually compensated by enabling a high harmonic rf structure properly tuned in amplitude and phase. This approach is however not straightforward, e.g., in C-band and X-band linacs. In this Letter we demonstrate that the longitudinal self-induced field excited by the electron beam itself is able to linearize the compression process without any use of high harmonic rf structure. The method is implemented at the FERMI linac, with the resulting high quality beam used to drive the seeded free-electron laser during user experiments.