Data-intensive scientific and commercial applications increasingly require frequent movement of large datasets from one site to the other(s). Despite growing network capacities, these data movements rarely achieve the promised data transfer rates of the underlying physical network due to poorly tuned data transfer protocols. Accurately and efficiently tuning the data transfer protocol parameters in a dynamically changing network environment is a major challenge and remains as an open research problem. In this paper, we present predictive end-to-end data transfer optimization algorithms based on historical data analysis and real-time background traffic probing, dubbed HARP. Most of the previous work in this area are solely based on real time network probing which results either in an excessive sampling overhead or fails to accurately predict the optimal transfer parameters. Combining historical data analysis with real time sampling enables our algorithms to tune the application level data transfer parameters accurately and efficiently to achieve close-to-optimal end-to-end data transfer throughput with very low overhead. Our experimental analysis over a variety of network settings shows that HARP outperforms existing solutions by up to 50% in terms of the achieved throughput.