This paper describes the concept of an FPGA-based digital camera trigger for imaging atmospheric Cherenkov telescopes, developed for the future Cherenkov Telescope Array (CTA). The proposed camera trigger is designed to select images initiated by the Cherenkov emission of extended air showers from very-high energy (VHE, E>20 GeV) photons and charged particles while suppressing signatures from background light. The trigger comprises three stages. A first stage employs programmable discriminators to digitize the signals arriving from the camera channels (pixels). At the second stage, a grid of low-cost FPGAs is used to process the digitized signals for camera regions with 37 pixels. At the third stage, trigger conditions found independently in any of the overlapping 37-pixel regions are combined into a global camera trigger by few central FPGAs. Trigger prototype boards based on Xilinx FPGAs have been designed, built and tested and were shown to function properly. Using these components a full camera trigger with a power consumption and price per channel of about 0.5 W and 19 Euro, respectively, can be built. With the described design the camera trigger algorithm can take advantage of pixel information in both the space and the time domain allowing, for example, the creation of triggers sensitive to the time-gradient of a shower image; the time information could also be exploited to online adjust the time window of the acquisition system for pixel data. Combining the results of the parallel execution of different trigger algorithms (optimized, for example, for the lowest and highest energies, respectively) on each FPGA can result in a better response over all photons energies (as demonstrated by Monte Carlo simulation in this work).