As you mentioned, it is a "reputed" IT firm. And you know this to be true first-hand. So, your concerns should be reduced a little.
The fact that a "reputed" organization is sending out unsigned offer letters is another question. Your definition of what "reputed" means and how this is demonstrated is something that only you know.
Either way, the tactic for handling this is to write a detailed acceptance letter which includes
all of the details of the offer and also mentions that this is in response to the offer letter recieved on {date} by {name}. Make sure to send this back to the organization in a way that produces a receipt or proof that they got it.
So now, you will have (1) the email transmission, (2) the hard copy, (3) your acceptance letter and (4) the mailing receipt. These four things will serve as your evidence of the offer and acceptance process.
Good luck!
P.S. One more thing. Before you submit your resignation, make sure you have spoken with the new group and analzye their response to your acceptance letter. If the letter makes them nervous, then you have something to worry about. Proceed with caution
