Summary: We obtain the exact non-perturbative thresholds of \(R^4\) terms in type IIB string theory compactified to eight and seven dimensions. These thresholds are given by the perturbative tree-level and one-loop results together with the contribution of the D-instantons and of the \((p,q)\)-string instantons. The invariance under \(U\)-duality is made manifest by rewriting the sum as a non-holomorphic-invariant modular function of the corresponding discrete U-duality group. In the eight-dimensional case, the threshold is the sum of an order-1 Eisenstein series for SL\((2,\mathbb{Z})\) and an order-3/2 Eisenstein series for SL\((3,\mathbb{Z})\). The seven-dimensional result is given by the order-3/2 Eisenstein series for SL\((5,\mathbb{Z})\). We also conjecture formulae for the non-perturbative thresholds in lower-dimensional compactifications and discuss the relation with M-theory.