Speaking outside her new official resident, No 10 Downing Street, after her appointment Ms May said that as Britain left the European Union it would forge a bold new role for itself in the world.
She also said her Conservative government would work not for the priviledged few but for everyone.
"The government I lead will not 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..""
Outgoing British Prime Minister David Cameron thanked his family and wished his successor Theresa May well in her new position.
The 49 year old resigned after voters rejected his advice and decided to leave the European Union.
Earlier during a packed House of Commons for his final parliamentary question time, Mr Cameron took time for a little humour.
"Mr Speaker, this morning I had meetings with ministerial colleagues and others. Other than one meeting this afternoon with Her Majesty The Queen, the diary for the rest of my day is remarkably light."
