This paper presents IRIS-BLAS, a novel heterogeneous and performance portable BLAS library. IRIS-BLAS is built on top of the IRIS runtime and multiple vendor and open-source BLAS libraries. It can transparently use all the architectures/devices available in a heterogeneous system, using the appropriate BLAS library based on the task mapping at run time. Thus, IRIS-BLAS is portable across a broad spectrum of architectures and BLAS libraries, alleviating the worry of application developers about modifying the application source code. Even though the emphasis is on portability, IRIS-BLAS provides competitive or even better performance than other state-of-the-art references. Moreover, IRIS-BLAS offers new features such as efficiently using extremely heterogeneous systems composed of multiple GPUs from different hardware vendors.