Silicon photonics is becoming a mainstream data-transmission solution for next-generation data centers, high-performance computers, and many emerging applications. The inefficiency of light emission in silicon still requires the integration of a III/V laser chip or optical gain materials onto a silicon substrate. A number of integration approaches, including flip-chip bonding, molecule or polymer wafer bonding, and monolithic III/V epitaxy, have been extensively explored in the past decade. Here, we demonstrate a novel photonic integration method of epitaxial regrowth of III/V on a III/V-on-SOI bonding template to realize heterogeneous lasers on silicon. This method decouples the correlated root causes, i.e., lattice, thermal, and domain mismatches, which are all responsible for a large number of detrimental dislocations in the heteroepitaxy process. The grown multi-quantum well vertical p-i-n diode laser structure shows a significantly low dislocation density of 9.5 × 104 cm-2, two orders of magnitude lower than the state-of-the-art conventional monolithic growth on Si. This low dislocation density would eliminate defect-induced laser lifetime concerns for practical applications. The fabricated lasers show room-temperature pulsed and continuous-wave lasing at 1.31 μm, with a minimal threshold current density of 813 A/cm2. This generic concept can be applied to other material systems to provide higher integration density, more functionalities and lower total cost for photonics as well as microelectronics, MEMS, and many other applications.