We examine the velocity profile of coherent vortices appearing as a consequence of the inverse cascade of two-dimensional turbulence in a finite box as a consequence of external pumping. We demonstrate that the coherent vortex corresponds to a passive regime of fluctuations. Then the flat velocity profile of the coherent flow is realized, as is demonstrated for two limit cases: short correlated in time pumping and static pumping. In the first case an explicit expression for the coherent velocity is obtained, in the second case we found that the coherent velocity is proportional to the 4/3 power of the pumping force.