We propose a consistent setup for the holographic dual of the strongly coupled large-Nc N=4 super Yang-Mills theory plasma which undergoes the Bjorken flow relevant to the quark-gluon plasma at BNL Relativistic Heavy Ion Collider and CERN LHC. The dual geometry is constructed order by order in a well-defined late-time expansion. The transport coefficients are determined by the regularity of the geometry. We prove, for the first time, that the dual geometry has an apparent horizon, hence, an event horizon, which covers a singularity at the origin. Further we prove that the dual geometry is regular to all orders in the late-time expansion under an appropriate choice of the transport coefficients. This choice is also shown to be unique. Our model serves as a concrete well-defined example of a time-dependent anti-de Sitter-space/conformal-field-theory dual.