The Extragalactic Background Light (EBL) can be probed via the absorption imprint it leaves in the spectra of gamma-ray sources ($\gamma\gamma \rightarrow e^-e^+$). We recently developed a dedicated technique to reconstruct the EBL, and its evolution with redshift, from $\gamma$ ray optical depth data using a large sample of blazars detected by the $Fermi$ Large Area Telescope. Here, we extend this dataset to the TeV regime using ground-based Cherenkov observations of 38 blazars and report the first homogeneous measurement of the EBL spectral intensity covering the ultraviolet to infrared wavelengths ($\sim$0.1-100$\mathrm{\mu m}$). A minimal EBL throughout the wavelength range with respect to integrated galaxy light is found, allowing little additional unresolved emission from faint or truly diffuse populations setting an upper limit of $\lesssim 4~{\rm nW\cdot m^{-2}sr^{-1}}$ at 1.4 ${\rm \mu m}$. In particular, the cosmic optical background (COB) at $z=0$ is found to be $27.8_{-2.0}^{+2.1}~{\rm nW\cdot m^{-2}sr^{-1}}$. This work lays the foundation for accurate gamma-ray measurements of the EBL across its whole spectral range using a combination of GeV and TeV data.