His club confirmed that San Siro club had met the midfielder’s release clause.
The Nerazzurri have agreed to pay 24million euros to sign the midfielder.
The 25-year-old had agreed a four-year contract worth 2.5million euros per season, and arrived Milan last night.
Vecino played 31 Serie A games for Fiorentina last season.
He will become the second Fiorentina midfielder to make the move to Inter this summer, after Borja Valero joined.