Wolves did not disclose specific financial details but said Neves, who signed his deal in Paris, was moving for a club record fee, reported to be worth €55 million ($60m).
“No other player has made such an impact on the pitch in gold and black during the last six years having featured more than 250 times in a remarkable period in the club’s history,” Wolves said in a statement.
The midfielder scored 30 goals in 253 appearances in all competitions with Wolves.
The 26-year-old joined Wolves in 2017 when they were in the second-tier Championship, helping them reach the top flight in his first season. He was previously with Porto in Portugal.
Wolves finished seventh in their first campaign back in the Premier League to qualify for the Europa League.
“What an unbelievable journey. A big thank you to every single person I had the chance to work with, every single moment was unforgettable,” a tearful Neves said in an emotional farewell video.
“To all of the players who were part of the club during the last six years, you are friends for life. The way we protected the pack was really incredible.
“I leave as a player, but I will always be a wolf. No matter what. Thank you for everything, and I will see you in the South Bank stadium, one day.”
The former Wolves captain had a year left on his contract and had also been linked with a move to Barcelona for next season.
Several high-profile players have been linked with moves to Saudi Arabia in recent weeks. Al Hilal also sought to sign Lionel Messi, with the Argentine great ultimately deciding to join Major League Soccer side Inter Miami.
Neves, capped 40 times by Portugal, will meet up in the Saudi league with compatriot Cristiano Ronaldo, who joined Al Nassr in December.
Al Hilal are the most decorated club in Saudi Arabia and Asia having won 66 trophies and hold the record for league and Asian Champions titles with 18 and four respectively.
Boosting the squad is a priority for the Riyadh-based club, who have lost their league and Champions League crowns. Spanish media report that they are also keen on Chelsea defender Kalidou Koulibaly and Manchester City midfielder Bernardo Silva.