The Ballon d'Or-winning striker, who joined the Spanish giants from Lyon in 2009, will depart on a free transfer when the season ends.
Benzema, who had a year left on his contract, is set to move to Saudi Arabia after receiving a "record offer" from Al-Ittihad, according to Spanish football journalist Guillem Balague.
Benzema, 35, won five Champions Leagues and four La Liga titles with Madrid.
Saudi state-run Al Ekhbariya television station reported on Sunday that Benzema will sign a two-year deal with Al-Ittihad.
Real boss Carlo Ancelotti had said on Saturday that he expected the former French international to stay next season.
"Benzema as been an example of behaviour and professionalism, and has represented the values of our club," Madrid said in a statement on Sunday. "He has earned the right to decide his future."
He is the third first-team player confirmed to be leaving Madrid in two days, after it was announced on Saturday that both Eden Hazard and Marco Asensio will also depart this summer.
Speaking on Saturday, Ancelotti said: "Kane is a great player, he is from Tottenham and we have to respect both the player and the club."
- Mat South innovates to boost COVID-19 vaccine uptake
- Building narratives: Nurse pens anti-child marriages fiction novel
- Building narratives: Chindiya empowers girls through sports
- The Soccer Whiz: The renaissance of the twilight years!
The Frenchman won a total of 25 major titles with Real Madrid, a record for the club.
Benzema is the Ballon d'Or holder, having guided Madrid to the Champions League title last season with 15 goals in the competition.
Also among his titles were five Club World Cups and three Copa del Rey triumphs.
Benzema, who has made 647 appearances for Madrid, is the second on their all-time goalscoring list with 353 - only Cristiano Ronaldo has more.
He is set to make his final Madrid appearance on Sunday against Athletic Bilbao, their final match of the 2022-23 La Liga season.
"Madridistas and all the fans around the world have enjoyed his magical and unique football, which has made him one of the great legends of our club and one of the great legends of world football," the club added.
"Real Madrid is and will always be his home, and we wish him and all his family the best in this new phase of his life."
Madrid will finish second in La Liga if they win on Sunday - but they are 11 points behind champions Barcelona and have failed to retain their Champions League title after being beaten in the semi-finals by Manchester City.
Those disappointments have led to many changes being rumoured at Santiago Bernabeu this summer - with Benzema's departure among the most seismic.
Ancelotti had said on Saturday that he had "no doubts" Benzema would stay, and Benzema himself claimed "the internet is not reality" when asked about his future on Thursday.
With a number of key players leaving, Real will need to bring in a new striker.
Balague says Spanish striker Joselu could join on loan from Espanyol, while Ancelotti is a fan of Tottenham striker Harry Kane. Real are also planning on a move for Paris St-Germain forward Kylian Mbappe next summer.