Heterogeneous network (HetNet) comprises multiple radio access technologies (RATs) allowing a user to associate with a specific RAT and steer to other RATs in a seamless manner. To cope up with the unprecedented growth of data traffic, mobile data can be offloaded to wireless fidelity (WiFi) in a long term evolution (LTE) based HetNet. In this paper, an optimal RAT selection problem is considered to maximize the total system throughput in an LTE-WiFi system with offload capability. Another formulation is also developed where maximizing the total system throughput is subject to a constraint on the voice user blocking probability. It is proved that the optimal policies for the association and offloading of voice/data users contain threshold structures. As a policy search over the entire policy space may become computationally inefficient, we propose computationally efficient algorithms based on the threshold structures for the association and offloading of users in LTE-WiFi HetNet. Simulation results are presented to demonstrate the voice user blocking probability and the total system throughput performance of the proposed algorithms in comparison with other benchmark algorithms.