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We present a comprehensive analysis of the host galaxies of 11 luminous fast blue optical transients (LFBOTs). We model new and archival host photometry and spectroscopy with Prospector. We determine that all LFBOT hosts are actively star-forming with recent bursts of star formation and have a median stellar mass of <inline-formula> <mml:math><mml:mi>log</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mrow><mml:mi>M</mml:mi></mml:mrow><mml:mrow><mml:mo>*</mml:mo></mml:mrow></mml:msub><mml:mo>/</mml:mo><mml:msub><mml:mrow><mml:mi>M</mml:mi></mml:mrow><mml:mrow><mml:mo>⊙</mml:mo></mml:mrow></mml:msub><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mn>9.6</mml:mn><mml:msubsup><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mo>−</mml:mo><mml:mn>1.61</mml:mn></mml:mrow><mml:mrow><mml:mo>+</mml:mo><mml:mn>0.74</mml:mn></mml:mrow></mml:msubsup></mml:math> </inline-formula>, present-day star formation rate SFR = <inline-formula> <mml:math><mml:mn>0.9</mml:mn><mml:msubsup><mml:mrow><mml:mn>9</mml:mn></mml:mrow><mml:mrow><mml:mo>−</mml:mo><mml:mn>0.95</mml:mn></mml:mrow><mml:mrow><mml:mo>+</mml:mo><mml:mn>14.85</mml:mn></mml:mrow></mml:msubsup></mml:math> </inline-formula> M<SUB>⊙</SUB> yr<SUP>−1</SUP>, and gas-phase oxygen abundance metallicity 12+log(O/H) = <inline-formula> <mml:math><mml:mn>8.5</mml:mn><mml:msubsup><mml:mrow><mml:mn>9</mml:mn></mml:mrow><mml:mrow><mml:mo>−</mml:mo><mml:mn>0.22</mml:mn></mml:mrow><mml:mrow><mml:mo>+</mml:mo><mml:mn>0.18</mml:mn></mml:mrow></mml:msubsup></mml:math> </inline-formula>. To contextualize these results, we compare them to the host properties of hydrogen-poor superluminous supernovae (SLSNe-I), several core-collapse supernova (CCSN)subtypes (SNe Ibc, II, and Ibn), and long gamma-ray bursts (LGRBs). We find that LFBOT hosts are more star-forming than CCSN hosts, but less star-forming than SLSN-I hosts. We further show that LFBOT hosts are more metal-poor than SN Ibc and II hosts, but more metal-rich than SLSN-I and LGRB hosts. Finally, we find that, similar to SLSNe-I and unlike CCSNe and LGRBs, a large fraction of LFBOTs occur in their hosts' faintest pixel or outside their host galaxy's light. Our results indicate that LFBOTs have a massive stellar origin that does not trace active star-forming regions within their hosts and have a weaker metallicity-dependence than other extreme transients. For these reasons, we favor a compact-object and Wolf─Rayet star merger progenitor scenario over other previously proposed models, such as tidal disruption events and failed or successful CCSN. Future discoveries of LFBOTs with the Rubin Observatory will help to increase their sample size and place firmer constraints on their environments and progenitors.