The 26-year-old Portuguese midfielder Neves had a year left on his contract.
He said at the end of last season he was ambitious amid interest from Barcelona.
However, Barca have not been able to come up with an acceptable offer and Neves has taken the option of becoming the latest big-name player to join the Saudi league.
Karim Benzema completed a free transfer to Al Ittihad this month and Chelsea midfielder N’Golo Kante is linked with joining him, while Cristiano Ronaldo moved to Al Nassr in December.
Wolves regard it as excellent business at a time where they are trying to generate funds for manager Julen Lopetegui to strengthen his squad.
Neves has been central to their success since joining from Porto in 2017.
He helped them win the Championship a year later and then to two consecutive seventh-placed finishes in the Premier League.
The club also reached the Europa League quarter-finals in 2020 – where they were knocked out by Lopetegui’s Sevilla – but have struggled to replicate that success and finished 13th last season having been bottom at Christmas.
Neves has made 253 appearances for Wolves in all competitions, scoring 30 goals.