I just an offer to study a master degree at a very good university. However I have recently been applying for jobs as well, and I was contacted by the HR of a company. Basically should I them that I have been given this offer? PS The degree is quite relevant to the nature of the company
From HR's perspective I don't think it'd be any different than your having a competing offer from another company on the table.
At most it might encourage them to expedite their decision process. However since the school year is probably still at month and a half or two months from starting they've probably got enough lead time that it wouldn't seem more urgent to them than normal.
I am assuming that you don't face any major deadlines prior to the start of the school year. If you need to move, make a large non-refundable deposit, or otherwise commit yourself heavily before then you should bring that date or dates up with your HR contact.