The video chats will be broadcast live on Google+ and on the London 2012 section of the New York Times site, where the conversations can be replayed.
The six Olympics hangouts will be hosted by New York Times journalists and "select fan participants", according to a Google+ post. Other fans can submit questions via Google+ and Twitter before and during the events using the hashtag #london2012hangout.
The first hangout is today (11 July) at 6pm New York time (11pm UK time) and they run until 17 July.
The New York Times has been experimenting with Google+ Hangouts, with the opinion team and others using the video chat option to engage with audiences.