Thompson, who led Drax for 12 years while it underwent a major transformation away from coal burning power plants, will first join the board of Tullow as a non-executive director and chair-designate following the group's annual general meeting on 25 April.
Previous to Drax, which once operated Europe's largest coal-fired power station, Thompson managed power firm InterGen's European buisness and was the head of project finance at PowerGen, the predecessor to energy firm E.On. Thompson also had stints at CDC Capital Partners, the private sector arm of the government's aid programme and the Bank of Botswana.
Heavey said Thompson has "exactly the right mix of leadership, managerial, operational and financial experience that Tullow needs".
"I look forward to working closely with Dorothy during the transition period until she takes over as chair in July and I will follow Dorothy and Tullow's progress over the next few years with much interest," he added.
Paul McDade, the company's chief executive, added that Thompson will help position Tullow for future growth "in what remains an uncertain environment in our sector".
"We will need to ensure that the company not only delivers on the potential of its current assets but also seeks out new opportunities for growth," he said.
I am very pleased to be joining Tullow as the company emerges from the recent downturn in a strong position following the significant progress it has made over the past two years.
I am looking forward to working with Paul and the board as we focus on delivering the full potential of the company's world class portfolio and the return to value enhancing growth.
Thompson also works as a non-executive director of the court of the Bank of England and the New York-listed Eaton Corporation.