Transformation optics (TO) provides an unprecedented technique to control electromagnetic (EM) waves by engineering the constitutive parameters of the surrounding medium through a proper spatial transformation. In general, ideal transformation optical devices require simultaneous electric and magnetic responses along all three dimensions. To ease the practical implementation, previous studies usually made use of reduced parameters or other simplified approaches, which inevitably introduce extra reflection or unwanted phase shift. Up to today, experimental realizations of full-parameter transformation optical devices in free space are still quite limited. Here, a general design strategy is proposed to solve this problem. As a specific example, a full-parameter spatial-compression TO medium with constitutive parameters taking the diagonal form diag( a, a , 1/ a ) for the TM wave incidence was designed and realized experimentally. Such spatial-compression TO media were then applied to the implementation of an ideal omnidirectional invisibility cloak capable of concealing a large-scale object over a wide range of illumination angles. Both the simulation and experiment confirm that the cloak allows for nearly unity transmission of EM waves in the forward direction without introducing extra scattering or phase shift. This work constitutes an important stepping stone for future practical implementation of arbitrary full-parameter omnidirectional transformation optical devices.