Antonio Conte was reportedly interested in handing the veteran midfielder a one-year contract extension at San Siro.
The 35-year-old's deal is due to expire at the end of August and he posted a farewell message to the club on his official Twitter account.
Valero wrote: "It was an honour to wear these colours. Thanks for everything @Inter."
Valero joined Inter from Fiorentina in 2017 and made 100 appearances for the Nerazzurri, scoring five goals.
A return to Fiorentina could be in the offing for the Spaniard, while Genoa and Parma have also been credited with an interest.