Passively mode-locked lasers have been widely investigated as one of the effective methods to obtain ultrashort pulses. As an important part of passively mode-locked fiber lasers, the exploration of 2D material-based saturable absorber has become one of the hotspots in ultrafast photonics in recent years. Germanene, a novel 2D Dirac material, with ultrafast optical response and broadband optical absorption, is a promising alternative material for saturable absorber in mode-locked fiber lasers. In this paper, germanium nanosheets are prepared via liquid-phase exfoliated method, with the saturable absorption property systematically characterized in three major wavebands of the near-infrared region. The generation of ultrashort pulses based on germanene saturable absorber in fiber lasers is further realized, in a broad waveband (1000 nm) centered at 1061.1, 1559.3 and 1883.5 nm, respectively. In addition, noise-like pulses operation with central wavelength of 1558.6 nm is also obtained, and the formation of rogue waves is further demonstrated via statistical analysis. To the best of our knowledge, this is the first experimental verification of the broadband saturable absorption property of germanene-based devices, covering three major fiber laser wavelengths from 1.0 to 2.0 μm.