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Spin-triplet superconductors provide an ideal platform for realizing topological superconductivity with emergent Majorana quasiparticles. The promising candidate is the recently discovered superconductor UTe₂, but the symmetry of the superconducting order parameter remains highly controversial. Here we determine the superconducting gap structure by the thermal conductivity of ultra-clean UTe₂ single crystals. We find that the a axis thermal conductivity divided by temperature κ/T in zero-temperature limit is vanishingly small for both magnetic fields H||a and H||c axes up to H/H_c2 ~ 0.2, demonstrating the absence of any types of nodes around a axis contrary to the previous belief. The present results, combined with the reduction of the NMR Knight shift in the superconducting state, indicate that the superconducting order parameter belongs to the isotropic A_u representation with a fully gapped pairing state, analogous to the B phase of superfluid ³He. These findings reveal that UTe₂ is likely to be a long-sought three-dimensional (3D) strong topological superconductor characterized by a 3D winding number, hosting helical Majorana surface states on any crystal plane.