According to Sky Sport, Como triggered the €6 million release clause in Liberali's contract, with half of that fee going to AC Milan, who also held a 50% economic stake in the player.
Milan had offered more for the 2007-born midfielder, but Liberali chose to join Como regardless. He is set to sign a five-year contract worth €1 million net per season, plus bonuses.
The move adds to a busy transfer window for Como, who have also paid €60 million to keep Nico Paz at the club and have already signed Kaiki Bruno and Luis Milla this summer.
With incomings largely completed, attention at Como is turning towards trimming the squad and finding new clubs for players surplus to Fabregas's plans.
Alvaro Morata is among those whose future is now in question after a difficult debut season by the lake.
The 1992-born forward arrived a year ago as an experienced signing intended to raise the level of Como's attack, but finished the season without a single goal.
According to Sky Sport, Morata has emerged as a target for Deportivo La Coruna, who won promotion to LaLiga last season and have placed him on a shortlist that also includes Federico Vinas and Fabio Silva.
A return to Spain would mark a fresh start for Morata after a season in Italy that fell well short of expectations following his arrival with considerable fanfare.
Como's transfer business this summer has been shaped by two parallel tracks, with significant investment in incoming talent running alongside an effort to move on players who no longer fit Fabregas's plans, Morata among the most prominent names in that second category.
Liberali arrives with a reputation as one of the more promising young midfielders to emerge from Serie B football, and Como's willingness to match his release clause, even with Milan able to offer more, points to a clear plan for how he fits into Fabregas's squad.
The scale of the outlay on Nico Paz alone shows the level of ambition at Como this summer, with the club prepared to back up individual signings with a broader strategy to reshape the group around their most valuable assets.
Morata's situation, by contrast, illustrates the other side of that rebuild, with a big-name arrival now facing an early departure after failing to deliver the impact Como had hoped for when they brought him in.