Silicon-based color-centers (SiCCs) have recently emerged as quantum-light sources that can be combined with telecom-range Si Photonics platforms. Unfortunately, using conventional SiCC fabrication schemes, deterministic control over the vertical emitter position is impossible due to the stochastic nature of the required ion-implantation(s). To overcome this bottleneck toward high-yield integration, a radically innovative creation method is demonstrated for various SiCCs with excellent optical quality, solely relying on the epitaxial growth of Si and C-doped Si at atypically-low temperatures in an ultra-clean growth environment. These telecom emitters can be confined within sub-nm thick epilayers embedded within a highly crystalline Si matrix at arbitrary vertical positions. Tuning growth conditions and doping, different well-known SiCC types can be selectively created, including W-centers, T-centers, G-centers, and, especially, a so far unidentified derivative of the latter, introduced as G'-center. The zero-phonon emission from G'-centers at ≈1300nm can be conveniently tuned by the C-concentration, leading to a systematic wavelength shift and linewidth narrowing toward low emitter densities, which makes both, the epitaxy-based fabrication and the G'-center particularly promising as integrable Si-based single-photon sources and spin-photon interfaces.