Cormier will leave in the New Year to return to the US, and in a separate departure, Steve Stewart, the group's head of customer care, will leave around the same time.
The departures come as Neil Berkett, Virgin Media's acting head, sets about making his mark on the business to prove that he can ensure that the cable giant fulfils its potential.
The four-play operator, which offers cable television, broadband, mobile and internet services, had hoped that a rebranding last year under the Virgin name would mark a turnaround in its fortunes.
However, continuing weak performance and a messy legal spat with rival BSkyB have hindered progress. It led to Burch, Virgin Media's former chief executive, resigning this summer.
News of Cormier's departure comes hot on the heels of Virgin Media putting plans for a nationwide television service on ice, as the company scales back projects set in motion by Burch.
Berkett has implemented a strategy of "doing less properly", which means that Virgin will halt its plan to replicate its full range of services for the half of the UK population beyond the reach of its cable network.