We analyze the production and detection of the Higgs boson in the next generation of linear [ital e][sup +][ital e[minus]] colliders operating in the [ital e][gamma] mode. In particular, we study the production mechanism [ital e]+[gamma][r arrow][ital e][gamma][gamma][r arrow][ital e]+[ital H], where one photon is generated via the laser backscattering mechanism, while the other is radiated via the usual bremsstrahlung process. We show that this is the most important mechanism for Higgs boson production in a 500 GeV [ital e][gamma] collider for [ital M][sub [ital H]][approx gt]140 GeV. We also study the signals and backgrounds for detection of the Higgs boson in the different decay channels [ital b[bar b]], [ital W][sup +][ital W[minus]], and [ital ZZ], and suggest kinematical cuts to improve the signature of an intermediate-mass Higgs boson.