Heterogeneous platforms that include diverse architectures such as multicore CPUs, FPGAs and GPUs are becoming very popular due to their superior performance and energy efficiency. Besides heterogeneity, a promising approach for minimizing energy consumption is through approximate computing which relaxes the requirement that all parts of a program are considered equally important to the output quality, thus, all should be executed at full accuracy. Our work extends a traditional OpenMP-like programming model and runtime system to support seamless execution on hybrid architectures with approximation semantics. Starting from a common application code, annotated with our programming model, the programmer can not only target heterogeneous architectures comprising CPU, FPGA and GPU components, but can also regulate the amount of approximation. We evaluate our framework on a number of large-scale applications and demonstrate that the combination of heterogeneous and approximate computing can provide a powerful dynamic interplay between performance and output quality.