Step 1: Read the sentence carefully and note the time reference.
The phrase “by next year on the same day” indicates a fixed point of time in the future.
Step 2: When an action will be completed before or by a specific time in the future, we use the future perfect tense.
Step 3: The structure of the future perfect tense is:
will have + past participle.
Step 4: The past participle of celebrate is celebrated.
So, the correct verb form is will have celebrated.
Step 5: Therefore, the correct sentence is:
“They have completed 24 years of togetherness today and by next year on the same day, they will have celebrated their 25th anniversary.”