Vecino has signed a contract until 2021 with his new club, who have met his buyout clause.
Vecino made 85 appearances for Fiorentina, scoring six goals and providing eight assists.
A Uruguay international, the 25-year-old has won 13 caps for his country, scoring once.
"I'm delighted to have joined and it is a big challenge for me," Vecino told Inter's official website.
"I have been playing in Italy for a couple of years now. I am at a good age and have the right experience. I believe I will enjoy my time here.
"Besides being a top player [Valero] is a lovely guy and he'll definitely do well here because he has great ability."