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 creep remains poorly understood, and controversial. Here, we propose that concrete creep at RH (relative humidity) > 50%, but fixed moisture-contents (i.e., basic creep), arises from a dissolution-precipitation mechanism, active at nanoscale grain contacts, as is often observed in a geological context, e.g., when rocks are exposed to sustained loads, in moist environments. Based on micro-indentation and vertical scanning interferometry experiments, and molecular dynamics simulations carried out on calcium-silicate-hydrates (C-S-H's), the major binding phase in concrete, of different compositions, we show that creep rates are well correlated to dissolution rates - an observation which supports the dissolution-precipitation mechanism as the origin of concrete creep. C-S-H compositions featuring high resistance to dissolution, and hence creep are identified - analysis of which, using topological constraint theory, indicates that these compositions present limited relaxation modes on account of their optimally connected (i.e., constrained) atomic networks.