Novel Azimuthal Observables from Two-Photon Collision at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup><mml:msup>

In this Letter, we advocate a set of novel azimuthal-angle-related observables associated with exclusive hadron production from two-photon fusion at e^{+}e^{-} colliders, taking the γγ→ππ as a benchmark process. As a direct consequence of the linearly polarized quasireal photons emitted off the electron and positron beams, the cos2ϕ azimuthal asymmetry in dipion production is predicted within the transverse-momentum-dependent factorization framework. In numerical analysis, we take the helicity amplitudes of γγ→ππ determined from the partial wave solutions in dispersion relation as input, and find that the predicted cos2ϕ azimuthal modulation may reach 40% for the typical kinematical setup of Belle 2 and BESIII experiments. Future accurate measurement of this azimuthal asymmetry may facilitate the direct extraction of the relative phase between two helicity amplitudes with photon helicity configurations ++ and +-. This knowledge provides a valuable input for the dispersive determination of the hadronic light-by-light contributions.