How to correct plagiarism in my own Master's thesis, years later? My situation is somewhat similar to this question, but I'm the plagiarizer.

Six years ago I did my Master's degree by coursework at university X, and wrote the Master's thesis under supervision of well-known Prof. A. For many reasons that I don't want to list here, I plagiarized. The first part of my thesis was background, and the second part was the original contribution. 

In the background part, I copied an entire chapter from textbook T about algorithm S. Algorithm S was invented more than 50 years ago, and is described in several books, including the very well-known T. I didn't paraphrase at all, I started by citing T, and then copied the whole chapter word by word.

The contribution part is actually contribution. One year after I left the school, Prof. A found another student to extend it and published the extension with me as the second author. (The paper included the algorithm and experiment in my thesis, but I didn't write a single word of the paper.)

I have moved to university Y to do a PhD. I have published several papers in top conferences and have very good relationship with several well-known researchers. I want to advance in academia.

Will the Master's thesis destroy any possibility of a future academic career? If someone read my Master's thesis, it is very easy to recognize, since the part from the textbook is in perfect English, and the rest is in extremely poor English.

Can I contact the university to submit a revised Master's thesis which re-describes the algorithm S? This is the last thing I want to do.
I cannot tell you what the university will do if you confess; I am not employed in a position which would be involved in such a decision, and besides, I think that this will depend on cultural and legal factors, plus the personality of the decision makers in your case. 

But I still think that it is better if you confess. There are several reasons for it: 


Your own inner peace. By contemplating confession and posting here you show that you have matured and have higher integrity and a better understanding of academic rules and the seriousness of plagiarism than back when you submitted your thesis. If you don't confess, you will have to live with both 1)the guilt of not only having made the mistake once, but still actively deceiving people, 
and 2) the anxiety of being discovered someday. I have been on both sides of a "hidden guilt" situation (although when it was on academic matters, it concerned milder cases), and I can tell you from experience that it is a bad situation, especially for the person who feels guilty and dreads discovery. It burdens you with a stress which can permeate to many unrelated areas of your life and make you miserable. 
Your risk of discovery rises with time. Nowadays, universities start to routinely employ plagiarism software. Who knows what funky electronic agent will snuffle in your old thesis ten years from now? Twenty? What if such software becomes so ubiquitous and cheap that employers start running it on your old theses when you apply for a job? 
If you confess, you will suffer negative consequences - but not nearly as bad as if you are discovered by a third party. Confession, especially if you are repentant, shows that you are capable of feeling remorse, have high integrity, also courage, and are willing to take responsibility. Being caught makes people see you as a cold-blooded fraud not deterred by social emotions like guilt and remorse. This makes you dangerous to them and reduces their empathy for you. They are much more likely to be lenient if you confess than if you are caught by others. 
The later it comes out, the worse for you. If you are either caught, or confess yourself much later (e.g. because you notice the negative effects of guilt and anxiety - and yes, this happens, I have witnessed such late confessions), it will have negative effects on your career. But right now, you are at its beginning. 


You have relatively little to lose yet. If you wait until later, you will have much more to restore after such a reputation blow. 
The younger you are when it happens, the more time you have to build a solid career without having to start anew. At times when you advance into more leading positions, it would be better that this story is a thing of the past, forgotten by most, than that it hits you out of nowhere. 
The sooner you confess after the mistake, the less reputation you lose. The less time you carry the problem hidden around, the less callous you appear, and also people feel less deceived. 
Once it comes out, everybody who has relied on your thesis being correct will be miffed. The more your life progresses, the more this number of people grows. If you confess early, you limit this number. 

Your university is not interested in a public scandal. The dean doesn't want to open the morning paper and see a "university duped by brazen plagiarist" title. They will be unpleasantly surprised by a private confession too, but they will not feel that the situation is out of their control, or that the worst that can happen has already happened. They will have some incentive to cooperate with you, as long as you confess. If you are caught, their best strategy becomes to distance themselves from you and denounce you. 
Time has shown that redemption is more beneficial to society than punishment-as-deterrent. This has been repeatedly shown in many situations: religious context (most of the New Testament is based on it, even though many Christian churches have historically been on the side of harsh punishment), law enforcement (prisons which are pleasant for the prisoners show better reformation rates) and parenting. So many people who have advanced to leadership positions have the wisdom not to mete out severe punishment for misconduct. Especially if you indicate that you are unlikely to repeat the mistake (and a confession is a very important part of it), they can be lenient. There is no guarantee that the leaders of your university will share this belief, but it is not exceptionally rare either. 


They will still have to enforce some consequences. It would be both unfair to the students who played by the rules to get their degree, and damaging to the university's reputation to just let you have your degree when you did not follow all requirements for it. But they will not be vengeful, seeking to end your career. This is something which certainly happens when academic misconduct is caught much later by a third party after the fact, see the German examples Peter Jansson cites (and notice that in some cases for the German politicians, their plagiarism was limited to a few sentences), but also cases like this one in which a renowned professor's academic career came to an end after academic misconduct (although not plagiarism) was proven.

You may want to find support before you go straight to the people who have the most to lose from the news. The behavior of your current employer is also hard to predict (they might be legally required to terminate you if a Master's degree was required for your acceptance into the Ph.D. program), but if you think they will be on your side, you might want to talk to them first so, when you come to the university, you have somebody who can testify that your current level of work is as good as one of a person who obtained a Master's degree regularly. Especially if you have coauthored with somebody with a good standing in your community, they may be interested in helping you rather than having a publication in coauthorship with somebody whose reputation was destroyed (but gauge them as a person too, some people will prefer to just drop you and forget you). 

I hope everything turns out to the best for you. As Nikana Reklawyks said, we are all human and make mistakes. If you are willing to repair the damage yours caused, this makes you a better, not a worse, human being.