The high magnetic field pulsar PSR J1119-6127, detected from radio to high-energy wavelengths, underwent a magnetar-like outburst beginning on 2016 July 27. In this paper, we study the postoutburst multiwavelength properties of this pulsar from the radio to GeV bands and discuss its similarity with the outburst of the magnetar XTE J1810-197. In phase-resolved spectral analysis of 0.5-10 keV X-ray data collected in 2016 August, the on- and off-pulse spectra are both characterized by two blackbody components and also require a power-law component similar to the hard X-ray spectra of magnetars. This power-law component is no longer distinguishable in data from 2016 December. We likewise find that there was no substantial shift between the radio and X-ray pulse peaks after the 2016 X-ray outburst. The gamma-ray pulsation after the X-ray outburst is confirmed with data taken after 2016 December, and the pulse structure and phase difference between the gamma-ray and radio peaks (similar to 0.4 cycle) are also consistent with those before the X-ray outburst. These multiwavelength observations suggest that the reconfiguration of the global magnetosphere after the 2016 magnetar-like outburst continued for at most about 6 months. We discuss the evolution of the X-ray emission after the 2016 outburst with the untwisting magnetosphere model.