No Open Source license does that. Even the GNU GPL license allows one program to interact with another non-free program via pipes, sockets, streams etc.
While the licenses can't do this, there are Linux distributions where the distribution creators make a commitment to only including free software, for example the Debian main package repository.
Which licenses give me a guarantee that a software I'm installing is completely open-source, free of closed-source dependencies or components?
Unfortunately, a license cannot do that.
Here's the problem. Anyone can attach put any license file into their project repo that they want to. The text of the license file may assert that that everything in their ...
Not directly answering the question, but the Free Software Foundation maintains a list of Free GNU/Linux distributions here
Since in freedom 1 is stated that "Access to the source code is a precondition for this.", I believe that all the distributions listed there are fully open-source too (otherwise the precondition of freedom 1 would not hold)
As others have noted, someone distributing software cannot change substitute their license for whatever license a third part distributed the third-party software under. So no license can offer any assurance there's no third-party components with a more restrictive license.
There is no substitute for examining all third-party pieces and their licenses.
When I ...
I think technically speaking it's more likely that "free software" is a subset of "open-source software" because the freedoms of modification and distribution of such, as defined by FSF's four essential freedoms, require the access to the source code.
Nevertheless, as two institutions in the reality, FSF and OSI may have different ...