PSR J1012−4235 is a 3.1 ms pulsar in a wide binary (37.9 days) with a white dwarf companion. We detect, for the first time, a strong relativistic Shapiro delay signature in PSR J1012−4235. Our detection is the result of a timing analysis of data spanning 13 yr and collected with the Green Bank, Parkes, and MeerKAT Radio Telescopes and the Fermiγ-ray space telescope. We measured the orthometric parameters for Shapiro delay and obtained a 22σ detection of the h₃ parameter of 1.222(54) μs and a 200σ detection of ς of 0.9646(49). With the assumption of general relativity, these measurements constrain the pulsar mass (M_p = 1.44_−0.12^+0.13 M_⊙), the mass of the white dwarf companion (M_c = 0.270_−0.015^+0.016 M_⊙), and the orbital inclination (i = 88.06_−0.25^+0.28 deg). Including the early γ-ray data in our timing analysis facilitated a precise measurement of the proper motion of the system of 6.58(5) mas yr⁻¹. We also show that the system has unusually small kinematic corrections to the measurement of the orbital period derivative, and therefore has the potential to yield stringent constraints on the variation of the gravitational constant in the future.