The 35-year-old remained an active part of the Inter side last season, making 25 league appearances for Antonio Conte’s men.
He confirmed his departure from the Milan club on social media today with a short and succinct message.
Valero wrote: “It was an honour to wear these colours. Thanks for everything Inter.”
A return to Fiorentina, where he was a big fan favourite, is not to be ruled out either.
The one-time Spain international joined Inter from Fiorentina in 2017. He has played in Italy since 2012 when he swapped Villarreal for Florence.