Reinforcement learning (RL) enables sequential decision-making in complex and high-dimensional environments through interaction with the environment. In most real-world applications, however, a high number of interactions are infeasible. In these environments, transfer RL algorithms, which can be used for the transfer of knowledge from one or multiple source environments to a target environment, have been shown to increase learning speed and improve initial and asymptotic performance. However, most existing transfer RL algorithms are on-policy and sample inefficient, fail in adversarial target tasks, and often require heuristic choices in algorithm design. This paper proposes an off-policy Advantage-based Policy Transfer algorithm, APT-RL, for fixed domain environments. Its novelty is in using the popular notion of ``advantage'' as a regularizer, to weigh the knowledge that should be transferred from the source, relative to new knowledge learned in the target, removing the need for heuristic choices. Further, we propose a new transfer performance measure to evaluate the performance of our algorithm and unify existing transfer RL frameworks. Finally, we present a scalable, theoretically-backed task similarity measurement algorithm to illustrate the alignments between our proposed transferability measure and similarities between source and target environments. We compare APT-RL with several baselines, including existing transfer-RL algorithms, in three high-dimensional continuous control tasks. Our experiments demonstrate that APT-RL outperforms existing transfer RL algorithms and is at least as good as learning from scratch in adversarial tasks.