I work in Company A and I'm kind of the star there (I feel it is mainly due to political reasons). Recently, I received an offer from Company B and I decided to accept it. HR department in my current company pushed me to review my decision and propose conditions under which I would like to stay at company. 

I feel that offer from Company B is much better for my career (project is more interesting, company is also a better suit for me), but I don't want to burn bridges. How can I respond?
['https://workplace.stackexchange.com/questions/78863', 'https://workplace.stackexchange.com', 'https://workplace.stackexchange.com/users/-1/']
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> I decided to accept it.
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If you've already made your decision and accepted the other offer, it's OK to say that.

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> I have already accepted the offer from Company B and thus cannot consider any counter offer. My last day will be XX/XX/XXXX.
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The expectation is that once a job offer is accepted (in writing), that that's it. You wouldn't accept an offer and keep interviewing or keep negotiating the terms so it shouldn't offend your current employer that you aren't going back on your word to Company B. It isn't burning a bridge to be honest here.
You just have to spin up a bunch of nonsense that you probably don't mean. Something like, "While I am grateful for the opportunities that were presented to me during my time here - I feel that at this juncture its best for all parties if I move on" Then say something about how you will do all you can to transfer knowledge and help in the transition prior to your departure

Then in your exit interview you say a bunch of nice things and leave.