He replaces Philip Hammond, who becomes chancellor. Ex-Energy Secretary Amber Rudd is home secretary and Eurosceptic David Davis is the Brexit secretary.
Ex-chancellor George Osborne was fired, the BBC's Laura Kuenssberg said.
On arriving at Downing Street, Mrs May vowed to lead a government that works for all, not just the "privileged few".
The UK's second female prime minister promised to give people who were "just managing" and "working around the clock" more control over their lives.
