[subject] + 终于 + [verb phrase] + 了
终于 says something has happened at last, after waiting, trying or worrying. It goes after the subject and before the verb, and the sentence usually ends in 了.
The result is usually one the speaker wanted, so 终于 often carries relief.
It works with adjectives that describe a change, too.
最后 is "last" in a list or a sequence: the final step, or the last item. 终于 isn't about order. It says the wait is over, so it can't introduce the last point of a talk or a list.
Without 了 the event doesn't sound finished, and 终于 is left hanging.