I don't know about Open Source - but as far as I know it is a pretty new-fangled phenomenon that started to become popular around 1999, when Eric S. Raymond published "The Cathedral & the Bazaar" and the suits started to think about Open Source as a business model. I think the "Open source Definition" (by the OSI) surfaced around the same time.
This was more than a decade after Stallman's publication of the Gnu Manifesto (1985), which did a lot to both popularize and create a consistent philosophy for free software.
However, the concept of free software is a much older than that. The SIMTEL20 archives did host a large body a free software from late 1970ies, and hobbyist magazines like Dr. Dobb's Journal and People's Computing Company did champion free software from the early 1970ies (my own involvement with free software started about that time, and I've stayed with free software ever since). Whether these efforts can be called "popular" depends, they were popular in my circles, but YMMV.
Of course, if you look at it from an historical perspective, free software predates proprietary software. When you bought a mainframe in the 1950ies (that is before my time), it came with full source code and you had full access to it. I am told that it was quite normal to create highly customized runtime environments by adapting this source code to the needs of the organization.
Of course, in those early days, the concept of source code was not the same as today. I regard the The Story of Mel as a good retelling of the spirit of those early days.