For low-frequency radio astronomy, software correlation and beamforming on general purpose hardware is a viable alternative to custom designed hardware. LOFAR, a newgeneration radio telescope centered in the Netherlands with international stations in Germany, France, Ireland, Poland, Sweden and the UK, has successfully used software real-time processors based on IBM Blue Gene technology since 2004. Since then, developments in technology have allowed us to build a system based on commercial off-the-shelf components that combines the same capabilities with lower operational cost. In this paper we describe the design and implementation of a GPU-based correlator and beamformer with the same capabilities as the Blue Gene based systems. We focus on the design approach taken, and show the challenges faced in selecting an appropriate system. The design, implementation and verification of the software system shows the value of a modern test-driven development approach. Operational experience, based on three years of operations, demonstrates that a general purpose system is a good alternative to the previous supercomputer-based system or custom-designed hardware.