I have completed the task that was assigned to me.
'Assegnato' = as-sen-YA-to. The 'gn' makes a sound like 'ny' in 'canyon'.
Use this when reporting back to your supervisor after finishing work. It is more professional than simply saying 'ho finito' (I finished). It explicitly connects your work to the original assignment.
The passive construction 'mi era stato assegnato' is formal and precise, showing that you took ownership of a delegated task. This level of phrasing demonstrates grammatical competence and professionalism beyond basic Italian.
Ho portato a termine il progetto.
I have brought the project to completion.
Idiomatic; 'portare a termine' is the standard phrase for completing a project
Il lavoro è pronto per la revisione.
The work is ready for review.
Focuses on the next step; shows forward thinking
Ho finito. Posso passare al prossimo incarico?
I have finished. Can I move on to the next assignment?
More informal; shows initiative
In Italian offices it is common to present completed work in person rather than just sending an email. A quick drop-by to say the task is done shows courtesy and keeps the relationship warm.