Based in Warsaw, his main focus will be overseeing and aligning the network's agencies while improving creative output and winning new business.
Before his promotion, Hennessey was the chief executive of Lowe's China office. Before that, he was the chief executive at Lowe Vietnam.
Tony Wright, the Lowe Worldwide president and chief executive, said: "Tim has a clear brief to be uncompromising. With our leadership positions in Russia and Ukraine, this is a very exciting part of the world for Lowe and our clients."