We present EDIpack, an exact diagonalization package to solve generic quantum impurity problems. The algorithm, based on a generalization of the look-up method introduced by Lin and Gubernatis, enables a massively parallel execution of the matrix-vector linear operations required by Lanczos and Arnoldi algorithms. We show that a suitable Fock basis organization is crucial to optimize the inter-processors communication in distributed memory setup and, thus, to reach sub-linear scaling in sufficiently large systems. We discuss the algorithm in details, indicating how to deal with multiple-orbitals and electron-phonon coupling. Finally, we detail the download, installation and functioning of this package.