The 29-year-old goalkeeper signed a four-year deal.
Neto made 47 match appearances for Valencia, keeping 10 clean sheets.
He will replace Jasper Cillessen who joined Valencia yesterday for 35m euros.
The Brazilian goalkeeper has a buyout clause set at 200m euros (£179m).
Speaking about the move, the La Liga champions said:
The Brazilian goalkeeper has a large presence between the sticks,
His height, at almost two metres, combined with his agility, make Neto a goalkeeper who gives strikers very little net to shoot at.