This is huge news:

Introducing GOG Connect
GOG Connect

Important: You can connect only one Steam account with your GOG.com library. This process is permanent – choose wisely!

Important 2: If you own some of the games and Connect doesn't recognize them, press the Refresh button and wait a while (can be a few minutes, hours or even a day). The reason for this is that GOG is using the Steam API to scan your Steam library and the API has a limit on the number of calls it can make for a given period of time. If you're still having problems, refresh your GOG account (simply clicking the link is enough; this is different that the Refresh button on the GOG Connect page!).

Important 3: In case you are still getting the message "Due to exceedingly high demand this may take up to several days, please check back later. Thank you for your patience." after waiting a while and trying the account refresh link above, then it would be a good idea to contact GOG support. Many users have reported that their problem was fixed quickly after that.

Connect your Steam account and grow or jumpstart your GOG.com library.

Today, we're launching a new program called GOG Connect. The premise is simple: connect your Steam account and add your eligible games to your GOG.com library.

Whether you're checking us out for the first time or have been with us for a while, GOG Connect gets you DRM-free versions of your games, digital extras, and a whole lot of freedom of choice (like whether you go with the GOG Galaxy client or not). It gets you our take on game ownership, and we say: why buy the games more than once?

While GOG Connect will stick around, the available games will come and go. These are limited-time offers made possible by participating developers and publishers, so stay tuned as we bring new titles onboard in the future (and grab your copies before they go away)!

I really hope more games are made available, because this could raise GOG's popularity significantly!

Edit on 29-April-2020:

Thanks to BrianFarnet: The GOG Connect Steam group is a useful way to get notified about future batches in your activity feed.