Following its flyby and first imaging of the Pluto-Charon binary, the New Horizons spacecraft visited the Kuiper belt object (KBO) 2014 MU69 (also known as (486958) Arrokoth). The imaging showed MU69 to be a contact binary that rotates at a low spin period (15.92 hours), is made of two individual lobes connected by a narrow neck and has a high obliquity (about 98 degrees)1, properties that are similar to those of other KBO contact binaries inferred through photometric observations2. However, all scenarios suggested so far for the origins of such configurations3-5 have failed to reproduce these properties and their probable frequent occurrence in the Kuiper belt. Here we show that semi-secular perturbations6,7 operating on only ultrawide KBO binaries close to their stability limit can robustly lead to gentle, slow binary mergers at arbitrarily high obliquities but low rotational velocities, reproducing the characteristics of MU69 and other similar oblique contact binaries. Using N-body simulations, we find that approximately 15 per cent of all ultrawide binaries with a cosine-uniform inclination distribution5,9 are likely to merge through this process. Moreover, we find that such mergers are sufficiently gentle to deform the shape of the KBO only slightly. The semi-secular contact binary formation channel not only explains the observed properties of MU69, but may also apply to other Kuiper belt or asteroid belt binaries and in the Solar System and extra-solar moon systems.