Financial details were not disclosed, but British media reported the Saudi side paid the Premier League club 40 million pounds ($52.50 million) to sign Toney until 2028.
"It's been a pleasure to work with Ivan over the last four years," coach Thomas Frank said.
"It's a wonderful journey that we have been on together. Ivan helped the club and the team, and the club and the team have helped Ivan.
"I'm happy he has an opportunity to try something new in his life and career. We thank him for so many magic moments and wish him all the best for his next chapter. Ivan leaves as a Brentford legend."
Toney had been a key figure at Brentford and had been instrumental in their promotion from the second-tier Championship to the top flight in 2020-21 when he scored 33 league goals.
However, an eight-month ban for breaches of betting rules saw him miss a huge chunk of last season, and Brentford finally cashed in on the player who scored 72 goals in 141 appearances for the club.
Toney has also played six times for England, scoring one goal.