An advisory board will be set up and will include Adam Sampson, chief executive of homelessness charity Shelter, and Lesley Morphy, head of charity Crisis.
The foundation will research homelessness and its causes, including family breakdown, a lack of affordable housing and children leaving care and slipping through the net.
Cameron said: “Last December, 130,000 children woke up on Christmas Day without a stable roof over their head. That’s more than double the figure for 1997.”

He added: “I’m putting tackling poverty at the heart of my mission for the Conservative Party.”

The party said in 2004 it was committed to Labour's target of ending child poverty by 2020.