Context. Fossil groups (FGs) are galaxy aggregates with an extended and luminous X-ray halo, which are dominated by a very massive early-type galaxy and lack of L∗ objects. FGs are indeed characterized by a large magnitude gap between their central and surrounding galaxies. This is explained by either speculating that FGs are failed groups that formed without bright satellite galaxies and did not suffer any major merger, or by suggesting that FGs are very old systems that had enough time to exhaust their bright satellite galaxies through multiple major mergers. Aims: Since major mergers leave signatures in the stellar populations of the resulting galaxy, we study the stellar population parameters of the brightest central galaxies (BCGs) of FGs as a benchmark against which the formation and evolution scenarios of FGs can be compared. Methods: We present long-slit spectroscopic observations along the major, minor, and diagonal axes of NGC 6482 and NGC 7556, which are the BCGs of two nearby FGs. The measurements include spatially resolved stellar kinematics and radial profiles of line-strength indices, which we converted into stellar population parameters using single stellar-population models. Results: NGC 6482 and NGC 7556 are very massive (M∗ ≃ 1011.5 M⊙) and large (D25 ≃ 50 kpc) galaxies. They host a centrally concentrated stellar population, which is significantly younger and more metal rich than the rest of the galaxy. The age gradients of both galaxies are somewhat larger than those of the other FG BCGs studied so far, whereas their metallicity gradients are similarly negative and shallow. Moreover, they have negligible gradients of α-element abundance ratio. Conclusions: The measured metallicity gradients are less steep than those predicted for massive galaxies that formed monolithically and evolved without experiencing any major merger. We conclude that the observed FGs formed through major mergers rather than being failed groups that lacked bright satellite galaxies from the beginning. Based on observations made with the Gran Telescopio Canarias (GTC), installed in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias (IAC).Full Tables A.1-A.3 are only available in electronic form at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/618/A172