People aged between 18 and 24 can apply for funds, expected to typically be about £2,500, from StartUp Loans.
Mr Cameron said he hopes the initiative could lead to 30,000 more start-ups and give a boost to economic growth reports The BBC.
The loans must be repaid within five years, and interest will be charged at the level of the Retail Prices Index plus 3 per cent.
Mr Cameron said he wanted young people to have the confidence and support to turn “that spark of an idea into the next global brand”.
It comes as an enterprise review says the UK would have 900,000 more businesses if it had the same rate of entrepreneurship as the US.
The review, by former Conservative minister Lord Young of Graffham, said that “many don’t realise the opportunities that enterprise offers”.
Back in November 2010, Lord Young was rebuked by Mr Cameron for claiming most Britons had “never had it so good” despite the “so-called recession”.
Lord Young, who served in Margaret Thatcher’s cabinet in the 1980s, said on Monday that small businesses “are the engine room of our economy and critical to future economic growth.”
He added: “But we cannot be complacent. Now, more than ever, we have got to get behind our small businesses and encourage even more people to seize the opportunities and support that there is to start up on their own.”
The StartUp Loans scheme will be chaired by entrepreneur and Dragons’ Den participant James Caan, and administered by groups who already work with young people.
Mr Caan said the initiative “provides guidance, access to expertise and finance. These are the three vital ingredients for starting your own business.
“Armed with all of these, young people are already on the way to shaping their own future.”
Mr Cameron said: “I want this to be the year where people can think: yes, I can do it; that we can get as many viable businesses as possible off the ground, that people can have a go and that we see a whole new wave of entrepreneurs who start small but think big.”