Chief executive Andy Webb told us in a statement that the decision followed a "comprehensive review" in the wake of Russian carmaker Marussia's arrival as title sponsor and investor.
The statement said "it is readily apparent that the team must take major steps in order to accelerate its rate of improvement".
"Consequently, the decision has been taken that the team will take greater control of its own destiny," added Webb, revealing Virgin has therefore been "obliged to terminate our relationship" with Wirth and his company Wirth Research.
"Looking ahead, we will now be pursuing an alternative technical path and look forward to announcing our plans in more detail over the coming weeks," he said.
Webb however denied suggestions the split with Wirth means the computational fluid dynamics (CFD) approach has proved a failure, but left the door open to new options.
We maintain our absolute belief in CFD as a technology
"At this stage I would like to underline our continued commitment to a cost-efficient commercial model," he said.
"We maintain our absolute belief in CFD as a technology, especially since it continues to become more cost-effective with every year.
"Naturally, we will continue to use every means at our disposal to improve the aerodynamics of our car with immediate effect."