The 25-year-old, who joined the Florentine club 3-1/2 years ago from Uruguayan club Nacional, made 31 league appearances last season, scoring three goals.
Vecino is Inter's fifth signing in the summer transfer window and the second from Serie A rivals Fiorentina after fellow midfielder Borja Valero.
(Reporting by Silvia Recchimuzzi in Gdynia; Editing by Hugh Lawson)
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