In the intersecting braneworld models, higher curvature corrections to the Einstein action are necessary to provide a non-trivial geometry (brane tension) at the brane junctions. By introducing such terms in a Gauss–Bonnet form, we give an effective description of localized gravity on the singular delta-function branes. There exists a non-vanishing brane tension at the four-dimensional brane intersection of two 4-branes. Importantly, we give explicit expressions of the graviton propagator and show that the Randall–Sundrum single-brane model with a Gauss–Bonnet term in the bulk correctly gives a massless graviton on the brane as for the RS model. We explore some crucial features of completely localized gravity in the solitonic braneworld solutions obtained with a choice (ξ= 1) of solutions. The no-go theorem known for Einstein's theory may not apply to the ξ= 1 solution. As complementary discussions, we provide an effective description of the power-law corrections to Newtonian gravity on the branes or at the common intersection thereof.