The 25-year-old, who left Fiorentina for Germany in 2009, has signed a four-year deal at the San Siro.
Kuzmanovic said that he favoured a return to Serie A over a move to Spain with Valencia.
"I am happy to wear the Inter jersey," Kuzmanovic told TMW. "Valencia were interested, but my desire was always to return to Italy."
The deal is said to be worth around €2m (£1.7m).