The correct form to use is the present perfect, as in 'I have solved the problem.'
I have solved the problem. The correct form to use in this context is the present perfect.
The present perfect is used to describe acts that occurred in the past but are relevant to the present. The activity of addressing the problem has been finished in this situation, but the speaker is articulating the consequence or effect of that action in the present.
If a friend inquires about the problem, the speaker might respond, 'I have fixed the problem,' implying that the problem is no longer present or an issue.