The astrophysical origin of gravitational wave transients is a timely open question in the wake of discoveries by the Laser Interferometer Gravitational-Wave Observatory (LIGO)/Virgo. In active galactic nuclei (AGNs), binaries form and evolve efficiently by interaction with a dense population of stars and the gaseous AGN disk. Previous studies have shown that stellar-mass black hole (BH) mergers in such environments can explain the merger rate and the number of suspected hierarchical mergers observed by LIGO/Virgo. The binary eccentricity distribution can provide further information to distinguish between astrophysical models. Here we derive the eccentricity distribution of BH mergers in AGN disks. We find that eccentricity is mainly due to binary-single (BS) interactions, which lead to most BH mergers in AGN disks having a significant eccentricity at 0.01 Hz, detectable by the Laser Interferometer Space Antenna. If BS interactions occur in isotropic-3D directions, then 8%-30% of the mergers in AGN disks will have eccentricities at 10 Hz above e(10 Hz) greater than or similar to 0.03, detectable by LIGO/Virgo/Kamioka Gravitational Wave Detector, while 5%-17% of mergers have e(10 Hz) >= 0.3. On the other hand, if BS interactions are confined to the AGN-disk plane due to torques from the disk, with 1-20 intermediate binary states during each interaction, or if BHs can migrate to less than or similar to 10(-3) pc from the central supermassive BH, then 10%-70% of the mergers will be highly eccentric (e(10 Hz) >= 0.3), consistent with the possible high eccentricity in GW190521.