I remember meeting him yesterday

I remember meeting him yesterday. In this sentence, why is the gerund form of meet used instead of 'to meet'? Is there any rule for such use?

I remember meeting him yesterday.

The meaning is very dependent on your exact use of the present tense of remember. Although many comments have been addressing the question of a past tense or future form usage, this does not seem to help you in this instance.

The sentence implies a memory that is being recalled at the moment. Moreover, what is being remembered is an event or action in the past.

...and as we all know, a gerund can function very nicely in this situation.

So, a plausible scenario might include something like...

"Oh! Him! I remember meeting him just yesterday"

For me, a more natural usage would be in a situation like...

I remember locking the door, but I don't think I remembered to set the alarm...

Notice I sneaked in another dependent clause with remember in the past tense + "to" + the infinitive. It has another meaning, as pointed out in the comments. The "remembering" was in the past, and so was the action of meeting him.

Please note that "I remember to meet yesterday" is just not good English, and I cannot think of where it might be used.

For more examples demonstrating the differences between the usages see: https://www.crownacademyenglish.com/remember-infinitive-ing-form-gerund/......

or https://www.englishgrammar.org/ing-form-infinitive/