Benzema moves to Saudi Arabia after spending 14 years in the Spanish capital, winning five Champions League trophies and four La Liga titles among other honours.
The 35-year-old, who is the current holder of the Ballon D'or, scored 354 goals in 648 games for Real Madrid.
He marked his final Real Madrid appearance with a goal in the 1-1 draw with Athletic Bilbao on Sunday.
Benzema, who joined Real Madrid from Olympique Lyon in the summer of 2009, had one year remaining on his contract, but reached an agreement with his employers to leave early.
"I am excited to experience a new football league in a different country," the former France striker, who will wear the number 9 shirt, said.
"I have been fortunate to achieve amazing things in my career and achieve everything I can in Spain and Europe
"It now feels the time is right for a new challenge and project. I am looking forward to joining my new team-mates and, together with them, help take this amazing club and the game in Saudi Arabia to new levels."
Benzema won a club-record 25 trophies during his time as a Real Madrid player.
