Roll-to-roll manufacturing of CdTe solar cells on flexible metal foil substrates is one of the most attractive options for low-cost photovoltaic module production. However, various efforts to grow CdTe solar cells on metal foil have resulted in low efficiencies. This is caused by the fact that the conventional device structure must be inverted, which imposes severe restrictions on device processing and consequently limits the electronic quality of the CdTe layer. Here we introduce an innovative concept for the controlled doping of the CdTe layer in the inverted device structure by means of evaporation of sub-monolayer amounts of Cu and subsequent annealing, which enables breakthrough efficiencies up to 13.6%. For the first time, CdTe solar cells on metal foil exceed the 10% efficiency threshold for industrialization. The controlled doping of CdTe with Cu leads to increased hole density, enhanced carrier lifetime and improved carrier collection in the solar cell. Our results offer new research directions for solving persistent challenges of CdTe photovoltaics.