Speaking outside 10 Downing Street after being appointed by the Queen, she said it would be her mission to “build a better Britain”.
She promised to give people who were “just managing” and “working around the clock” more control over their lives.
Mrs May is the UK’s second female prime minister, after Margaret Thatcher.
Mrs May later began appointing Cabinet members, with Philip Hammond – foreign secretary under Mr Cameron – becoming chancellor and Boris Johnson becoming the new foreign secretary.
Mrs May’s husband Philip was standing behind her as she made her first public speech in the role, highlighting the “precious bond” between England, Scotland, Wales and Northern Ireland and between “every one of us”.
“That means fighting against the burning injustice that if you’re born poor you will die on average nine years earlier than others,” she said.
For an “ordinary working class family”, she added, “life is much harder than many people in Westminster realise”.
Speaking directly to people who were “just managing”, she said: “The government I lead will be driven, not by the interests of the privileged few, but by yours. We will do everything we can to give you more control over your lives.
“When we take the big calls, we’ll think not of the powerful, but you.
“When we pass new laws, we’ll listen not to the mighty, but to you. When it comes to taxes, we’ll prioritise not the wealthy, but you.Culled from bbc.