Long-term creep (i.e., deformation under sustained load) is a significant material response that needs to be accounted for in concrete structural design. However, the nature and origin of concrete creep remain poorly understood and controversial. Here, we propose that concrete creep at relative humidity ≥ 50%, but fixed moisture content (i.e., basic creep), arises from a dissolution-precipitation mechanism, active at nanoscale grain contacts, as has been extensively observed in a geological context, e.g., when rocks are exposed to sustained loads, in liquid-bearing environments. Based on micro-indentation and vertical scanning interferometry data and molecular dynamics simulations carried out on calcium–silicate–hydrate (C–S–H), the major binding phase in concrete, of different compositions, we show that creep rates are correlated with dissolution rates—an observation which suggests a dissolution-precipitation mechanism as being at the origin of concrete creep. C–S–H compositions featuring high resistance to dissolution, and, hence, creep are identified. Analyses of the atomic networks of such C–S–H compositions using topological constraint theory indicate that these compositions present limited relaxation modes on account of their optimally connected (i.e., constrained) atomic networks.