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Gravitational-wave observations of binary black holes provide a suitablearena to test the fundamental nature of gravity in the strong-field regime.Using the data of the inspiral of 29 events detected by the LIGO-Virgoobservatories, we perform a theory-agnostic test of the Kerr hypothesis. Wecompute the leading-order deviation to the gravitational waves emitted in thefrequency domain and provide constraints on two deformation parameters($\delta_1$ and $\delta_2$) belonging to a general class of axisymmetricnon-Kerr black hole spacetimes proposed by Konoplya, Rezzolla & Zhidenko. Ourstudy shows that all the analyzed events are consistent with the Kerrhypothesis. The LIGO-Virgo data provide stronger constraints on $\delta_1$ and$\delta_2$ than those obtained in our previous studies with X-ray data (PapersI and II), while, on the other hand, they cannot constrain the otherdeformation parameters of the Konoplya-Rezzolla-Zhidenko metric ($\delta_3$,$\delta_4$, $\delta_5$, and $\delta_6$).

Constraining the Konoplya-Rezzolla-Zhidenko deformation parameters III: limits from stellar-mass black holes using gravitational-wave observations