The funding will be used to acquire up to 330 properties which will be made available to Londoners who have been – or are at risk of – becoming homeless.
The properties will be let out at genuinely affordable rents to some of the most vulnerable Londoners.
Real Lettings Property Fund 2 will be run by social impact company Resonance Limited and homelessness charity St Mungo’s.
In addition to the £15m from City Hall, the London boroughs of Croydon, Lambeth and Westminster have committed £45m to the scheme.
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Mr Khan said: “The scale of homelessness in our capital is shocking and we are doing everything we can to tackle it.
“By providing opportunities for homeless Londoners to leave temporary emergency accommodation, we can help them move on with their lives in an affordable, stable home of their own.
“I will do all I can with local authorities, social enterprises and innovative new projects to help people who are homeless or sleeping rough – but we also need [the] government to play its part.
“They must fully fund services to help people who are homeless or at risk of becoming so, and tackle the long-term causes of homelessness, including by investing more in social housing and reconsidering many of their changes to the welfare system.”