Abstract We study the wide-binary eccentricity (e) distribution in young star clusters and the role of turbulence in setting the form of the e distribution using magnetohydrodynamical (MHD) simulations of star cluster formation. The simulations incorporate gravity, turbulence, magnetic fields, protostellar heating, and jets/outflows. We find that (1) simulations that employ purely compressive turbulence driving produce binaries with a superthermal e distribution (α > 1 in p(e)∝eα), while simulations with purely solenoidal driving or natural mixture of driving modes produce subthermal/thermal distributions (α ≤ 1), (2) the e distribution over the full range of binary separations in our simulations is set at the early stages of the star cluster formation process, (3) while binaries (separation of rpair ≤ 1000 AU) have subthermal to thermal e distributions (α ∼ 0.8), wide binaries (rpair > 1000 AU) have a superthermal distribution (α ∼ 1.8), and (4) low-mass binary systems (system masses of Msys ≤ 0.8 M⊙) have a highly superthermal distribution (α ∼ 2.4), whereas high-mass systems (Msys > 0.8 M⊙) exhibit a subthermal/thermal distribution (α ∼ 0.8). The binary eccentricity distribution is often modelled as a thermal distribution. However, our results suggest that the e distribution depends on the range of separation of the sampled binaries, which agrees with the findings from recent Gaia observations. We conclude that the dependence of the e distribution on the binary separation and mass is linked to the binary formation mechanism governed by the turbulent properties of the parent cloud.