Is it possible to get a researcher position in a prestigious institute with a degree from a not very well-ranked university? I'm currently in the 2nd year of my Ph.D. and I'm really interested in my future career options. I'm attending a double-degree study programme in two European universities, none of them being among the top ones. But, I'm employed as a researcher (not only a Ph.D. student) in a supercomputing center in one of them (member of PRACE, 3 years ago in top 40 from TOP500 list) since the beginning of my Master's degree, thanks to Dean's award for my Bachelor's thesis. Five years ago it was a top university in my country (slightly under 300 in QS WU rankings), but then the directorship changed and the ranking dropped drastically (to my shock completely out of QS WU rankings). The second university shares a pretty similar fate - from about 300th place to 520+ in the last 7 years (I have no idea, what happened), but still maintains at least 151-200 position in my field. In general, I feel, that while both of the labs I'm working in are good and productive, the problem lies in some other faculties who do not focus on research enough.

Is it possible to hope for admission into a researcher position in some well-ranked university in the future? I'm not talking only about post-doc now, but also in a long-time horizon. This situation makes me feel really inferior, so I'd like to now, if my researcher career direction is tightly bounded by this situation or if there is a possibility to overcome rankings with good research results over the years after Ph.D.
Yes, it is.

When you apply for a postdoc position several things will be important:


what you have done (i.e. does it fit with the future PI's research
agenda), 
how successful it was (i.e. did you publish your results
    in a top journal) and
you know what you want and you are burning for it


The name of the university might matter as well but once you graduated from your PhD your personal profile should be distinctive enough and the name does by far not matter as much as after your undergrads where everyone looks the same expect from the university name, marks average and some internship.