Central defender Vitorino Hilton has signed a one-year contract extension with Montpellier.
AC Milan have completed the permanent signing of defender Cristian Zapata from Villarreal for an undisclosed fee.
The 21-year-old is the sixth arrival at the City Ground this summer as they look to construct a competitive Championship squad.
Ayala sustained a knee injury last season which restricted him to just 10 appearances for the Canaries.
His switch to the Championship side will provide him with the opportunity to secure regular first-team football, something that could not be guaranteed at Carrow Road.
Forest chairman Omar Al Hasawi told the club's official website: "It is pleasing to have signed a player with such a wonderful pedigree.
"He's only 21 but has experienced life in the Premier League as well as in the Championship, and adds to the defensive resources at Sean O'Driscoll's disposal."
The Spain Under-21 international made five Premier League appearances for Liverpool before last summer's switch to Norwich in a £800,000 deal.