The 25-year-old Uruguay international has signed a four-year contract at San Siro, running until June 2021.
Vecino is the second player to leave Fiorentina for Inter this close-season, following the route plotted by Borja Valero, and he is the fifth signing made by new boss Luciano Spalletti.
"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."
Inter are aiming to bounce back from a disappointing 2016-17 campaign that saw them finish outside the European places in seventh.
A quick reunion is on the cards for Vecino and Valero as the Nerazzurri host Fiorentina in their season opener on August 20.