Volkswagen suggested Cox as a potential buyer when Cumberland announced it wanted to sell up.
David Cox, Cox Motor Group managing director, said: "Volkswagen were impressed with the way we handle our operations and asked if we would consider taking this step.
"While we will be building on the hard work that Ken and his team have put in over so many years, we will also be increasing the choice of new and used cars to benefit customers in this way also."
The new arm to the Group will be renamed and trade as Lancaster Volkswagen.
With the acquisition of Cumberland View, the employee count will be over 240 with turnover expected to exceed £65 million in 2008.
The Cox Motor Group was established eight years ago after Cox took over the then John Wild The Group. The group represents Honda, Renault, SsangYong, Citroen and Seat across its four sites in Blackpool, Kendal and Morecambe.