In this study, molecular beam epitaxial growth of strain-driven three-dimensional self-assembled Ge/GeSi islands on silicon-on-insulator (SOI) substrates, along with their optical and photodetection characteristics, have been demonstrated. The as-grown islands exhibit a bimodal size distribution, consisting of both Ge and GeSi alloy islands, and show significant photoluminescence (PL) emission at room temperature, specifically near optical communication wavelengths. Additionally, these samples were used to fabricate a Ge/GeSi islands/Si nanowire (NW) based phototransistor using a typical e-beam lithography process. The fabricated device exhibited broadband photoresponse characteristics, spanning a wide wavelength range (300-1600 nm) coupled with superior photodetection characteristics and relatively low dark current (~ tens of pA). The remarkable photoresponsivity of the fabricated device, with a peak value of ~11.4 A/W (λ ~ 900 nm) in the near-infrared (NIR) region and ~ 1.36 A/W (λ ~ 1500 nm) in the short-wave infrared (SWIR) region, is a direct result of the photoconductive gain exceeding unity. The room-temperature optical emission and outstanding photodetection performance, covering a wide spectral range from the visible to the SWIR region, showcased by the single layer of Ge/GeSi islands on SOI substrate, highlight their potential towards advanced applications in broadband infrared Si-photonics and imaging. These capabilities make them highly promising for cutting-edge applications compatible with complementary metal-oxide-semiconductor (CMOS) technology.