Dear Vikkh.Nitk,
Whenever a vacancy arises, the HR department is given a target to fill the vacancy within a certain time limit. They are given this recruitment-completion target in order to maintain operational continuity. Whenever an employee quits an organisation, a new one must join in the shortest possible time. A prolonged gap could hamper the operations which, in turn, could hamper customer satisfaction as well.
In your case your future company has gone a step ahead and has assured you a "joining bonus". This joining bonus was given to you so that you can quit your current company and losses caused to you could be offset either fully or partially.
Nevertheless, unthinkingly you gave assurance to the future employer on your early joining. Commitment to the future employer should have arisen from the commitment and that too in writing by the current employer. Now your current employer has refused to waive off the notice period and has asked you to serve the notice period. Their mandate has pushed you into the current predicament.
Far from forfeiture of the "joining bonus", a threat of revocation of the job offer itself is looming on your head. However, this threat could be imaginary as well. Send an email to the HR department of the future employer confirming your inability to join within a month. If required, you may go there personally and explain your inability. A personal meeting is always helpful.
Lastly, keep in mind the smooth exit from the current organisation as well. While you may insist on the early exit, you should not engage in an act that may be perceived as "misconduct" by the current employer. Any misconduct could be a double whammy to you.
Thanks,
Dinesh Divekar