The unidentified very-high-energy (VHE;E> 0.1 TeV)γ-ray source, HESS J1826−130, was discovered with the High Energy Stereoscopic System (HESS) in the Galactic plane. The analysis of 215 h of HESS data has revealed a steadyγ-ray flux from HESS J1826−130, which appears extended with a half-width of 0.21° ± 0.02_stat° ± 0.05_sys°. The source spectrum is best fit with either a power-law function with a spectral index Γ = 1.78 ± 0.10_stat± 0.20_sysand an exponential cut-off at 15.2_−3.2^+5.5TeV, or a broken power-law with Γ₁= 1.96 ± 0.06_stat± 0.20_sys, Γ₂= 3.59 ± 0.69_stat± 0.20_sysfor energies below and aboveE_br= 11.2 ± 2.7 TeV, respectively. The VHE flux from HESS J1826−130 is contaminated by the extended emission of the bright, nearby pulsar wind nebula, HESS J1825−137, particularly at the low end of the energy spectrum. Leptonic scenarios for the origin of HESS J1826−130 VHE emission related to PSR J1826−1256 are confronted by our spectral and morphological analysis. In a hadronic framework, taking into account the properties of dense gas regions surrounding HESS J1826−130, the source spectrum would imply an astrophysical object capable of accelerating the parent particle population up to ≳200 TeV. Our results are also discussed in a multiwavelength context, accounting for both the presence of nearby supernova remnants, molecular clouds, and counterparts detected in radio, X-rays, and TeV energies.