The supplementary planning guidance will allow developers of private land to bypass viability negotiations provided that a minimum of 35% of the development is affordable housing built without public funding.
For development on public land, 50% of the scheme is required to be affordable housing to qualify for the fast-track application.
Developments that fail to begin within two years of planning permission being granted, will undergo detailed scrutiny of their financial modelling.
The publication of the guidance follows an extensive consultation period.
Mr Khan said: “The housing crisis is the biggest challenge facing Londoners today with too many people – particularly the younger generation – being priced out of our city, unable to afford a home.
“I’ve been honest with Londoners from the start – we can’t turn things round overnight.
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“But we’re working hard to tackle the issue every day and we've already agreed to put £1.7bn of the investment that I secured from government into 50,000 new and genuinely affordable homes to rent and buy.
“This investment will work hand in hand with the new approach for developers that I’m introducing today, which will allow them to benefit from a fast track through the planning system if they offer more affordable housing and get building quickly.
“I’m determined to ensure we don’t have a repeat of what happened at Battersea Power Station, with developers unacceptably reducing the number of affordable homes on site after planning permission was granted.
“That’s why I’ve written to all councils offering City Hall’s expertise in robustly scrutinising applications to ensure we see the new and genuinely affordable homes built that Londoners desperately need.”
City Hall officials have urged local councils to contact the mayor's expert viability team if developers try to reduce affordable housing levels after planning permission has been granted.