COGARCH is an extension of the GARCH time series concept to continuous time, which has been suggested by Klüppelberg, Lindner, Maller (2004). We show that any COGARCH process can be represented as the limit in law of a sequence of GARCH(1,1) processes. As a by-product we derive the infinitesimal generator of the bivariate Markov process representation of COGARCH.