We present measurements of the B→ηKγ branching fractions and upper limits for the B→η′Kγ branching fractions. For B+→ηK+γ we also measure the time-integrated charge asymmetry. The data sample, collected with the BABAR detector at the Stanford Linear Accelerator Center, represents 232×106 produced BB̄ pairs. The results for branching fractions and upper limits at 90% confidence level in units of 10-6 are: B(B0→ηK0γ)=11.3-2.6+2.8±0.6, B(B+→ηK+γ)=10.0±1.3±0.5, B(B0→η′ K0γ)<6.6, B(B+→η′K+γ)<4.2. The charge asymmetry in the decay B+→ηK+γ is Ach=-0.09±0.12±0.01. The first errors are statistical and the second systematic. © 2006 The American Physical Society.