"The task of the new prime minister ... will be to get clarity on the question of what kind of relationship Britain wants to build with the European Union," Chancellor Angela Merkel told a news conference.
Her finance minister Wolfgang Schaeuble said clarity was needed quickly to limit uncertainty after Britain's shock choice for 'Brexit', which has rocked the 28-nation bloc and thrown decades of European integration into reverse.
May, 59, will on Wednesday replace David Cameron, who is resigning after Britons rejected his advice and voted on June 23 to quit the EU. On arriving and departing from Cameron's last cabinet meeting, she waved a little awkwardly from the doorstep of 10 Downing Street, shortly to become her home.
She will face the enormous task of disentangling Britain from a forest of EU laws, accumulated over more than four decades, and negotiating new trade terms while limiting potential damage to the economy.
The pound was up 1.2% against the dollar at around US$1.3150, boosted by the appointment of a new prime minister weeks earlier than expected after May's main rival dropped out.
But it remains more than 12% below the US$1.50 it touched on the night of the June 23 referendum, reflecting concerns that Brexit will hit trade, investment and growth.
The German leaders spoke after May's ally Chris Grayling appeared to dampen any hopes among Britain's EU partners that her rapid ascent might accelerate the process of moving ahead with the split and resolving the uncertainty hanging over the 28-nation bloc.