The authority did not say how much Vivendi would need to divest in either company but ordered the French group to present it with a "specific plan of action" within 60 days.
This might include an appeal to an Italian Regional Administrative Tribunal (TAR) and a formal complaint with the European Commission for violation of EU law, Vivendi said.
While AGCOM has ruled that Vivendi is in breach of Italian law, it has not specified exactly how much of a divestment in either of the two companies will be required.
Italy's communications regulator threw a wrench into Vincent Bollore's quest to expand his media empire, ruling the French billionaire can't keep both of the large stakes he has built up in Mediaset SpA and Telecom Italia SpA.
The decision marks a victory for Mediaset which has been battling with Vivendi in court after the group chaired by billionaire Vincent Bolloré previous year pulled out of an $860 million deal to buy Mediaset's pay-TV unit and a few months later gained a almost 30% stake, and significant shareholder voting rights in Mediaset, with rapid fire share purchases.More news: Blue Jackets beat Penguins 5-4 to avoid sweep
Vivendi now controls about 24% of Telecom Italia and 28.8% of Mediaset. Those laws were put in place when Berlusconi was prime minister to prevent dominance of a single media player.
Giordani said on Wednesday that Vivendi, which now holds a 28.8 percent stake in Mediaset, does have a relevant influence in the broadcaster's activities, in line with a ruling by an Italian regulator on Tuesday.
Vivendi has been attempting to tighten its grip on Telecom Italia and also began aggressively building its stake in Mediaset in December, when it only had a 3% stake in the company.
Vivendi released a statement on Tuesday saying that it "neither controls nor exercises a dominant influence on Mediaset" and said it was considering legal action.
In a statement, Vivendi said it was surprised by the ruling, adding that it had not violated Italian law in holding stakes in both companies. One scenario is that they could even perhaps revive the partnership that went sour after the Mediaset Premium deal, albeit in a different form.