The magnetized liner inertial fusion concept has been presented as a path toward obtaining substantial thermonuclear fusion yields using the Z accelerator [S. A. Slutz et al., Phys. Plasmas 17, 056303 (2010)]. We present the first integrated magnetohydrodynamic simulations of the inertial fusion targets, which self-consistently include laser preheating of the fuel, the presence of electrodes, and end loss effects. These numerical simulations provided the design for the first thermonuclear fusion neutron-producing experiments on Z using capabilities that presently exist: peak currents of Imax = 18–20 MA, pre-seeded axial magnetic fields of Bz0=10 T, laser preheat energies of about Elas = 2 kJ delivered in 2 ns, DD fuel, and an aspect ratio 6 solid Be liner imploded to 70 km/s. Specific design details and observables for both near-term and future experiments are discussed, including sensitivity to laser timing and absorbed preheat energy. The initial experiments measured stagnation radii rstag<75 μm, temperatures around 3 keV, and isotropic neutron yields up to YnDD=2×1012, with inferred alpha-particle magnetization parameters around rstag/rLα=1.7 [M. R. Gomez et al., Phys. Rev. Lett. (submitted)].