Get the copy that says the judgment is final
A divorce judgment only travels if it carries the court's note that no appeal is left. In Italy that note is the attestazione di passaggio in giudicato, added by the clerk. So how to legalize a Divorce Decree begins with asking for a certified copy that has it. The plain copy you were sent at the end of the case will not do the job.
A copy without that note is the commonest single reason a file is refused abroad. Registrars in other countries read a judgment as provisional until they see the wording. Look at your sheets now: if there is no note about finality, the copy is not the one to send. Order a fresh certified copy before anything else.
At the court clerk's window
The copy comes from the cancelleria, the clerk's office at the court that gave judgment. Bring the case number and the date, along with an identity paper. If a lawyer acted for you, their office holds the reference and can often order the copy faster than you can. Say that the copy is going abroad, so the clerk adds every stamp the file needs.
Consular legalization of a Divorce Decree in Italy cannot begin until the Procura has stamped that certified copy. Keep the whole copy together, seals and all, because the stamp covers the bundle rather than one sheet. Buy the €16 marca da bollo beforehand and hand it in with the papers.
Judicial paper, judicial desk
Italy splits legalization by the kind of paper. Administrative records go to the Prefettura, the state's provincial office, while judgments and notarial acts go to the Procura della Repubblica. A divorce judgment is a court act, so you legalize a Divorce Decree in Genoa at the Procura attached to the court. That is often the same courthouse that issued the copy.
Check what you actually hold
One caution before you set off. Not every Italian divorce ends in a court judgment; some are recorded at the comune instead, which produces a registry paper rather than a sentenza. If your document came from the registry, it is administrative and follows the Prefettura route. Read the letterhead and the signature block to see which of the two you have.
The consular link
The embassy legalization of a Divorce Decree in Genoa is the final link, done at the destination country's consulate in Italy. Their clerk stamps over the Procura mark, having compared it with the specimen they hold. Book the appointment, bring the original and a copy, and carry an identity paper. Many missions want a translation attached as well, so ask them first.
Whether the embassy attestation of a Divorce Decree in Genoa is needed depends on the country that will read the judgment, not on anything at this end. Some accept a single-step certification and stop there. Others will not register a marriage or a status change without their own stamp. Ask the receiving authority in writing and keep the answer with the papers.
Duty, timing and why people need it
Money splits along the same line as the stamps: €16 in duty here, then the mission's own charge abroad. From hand-over to return, count 10–15 business days, or 3–5 on the express route. People need this to remarry, to correct their status on a foreign register, for residence files and for inheritance claims. Where a wedding date is fixed, start early and take the express route.