It appears that CPMC construction has been approved. They were aiming for a completion date of October 2015 and operational start in February 2016, but it seems unlikely due to delays in getting approval. I still can't find a start date anywhere.

For more info, check out the following:

Renderings: http://rebuildcpmc.org/plans/stlukes_campus/

Project summary and detailed plans (PDF): http://www.sf-planning.org/index.aspx?page=2727

News articles: http://rebuildcpmc.org/latest/news/

For a deeper dive, here is an article from 2010 in the New York Times: http://www.nytimes.com/2010/07/30/us/30bcstlukes.html?pagewanted=all.

Take it with a grain of salt, as the writer makes it sound like St. Lukes is a ghost town, nearly as bad as SF General, which it's not. They didn't even mention the Women's Center!