The France striker has signed a deal with the Saudi champions until 2026 having brought his 14-year stay at Real Madrid to an end.
The move was announced on Tuesday evening, hours after Benzema's farewell press conference at Real Madrid.
"I'll never forget Real Madrid because it's impossible," he said.
"It's difficult to talk. There are so many emotions. I wanted to thank Real Madrid and my teammates. It's been a good journey in my life.
"I was lucky enough to fulfil my childhood dream thanks to the president, who a long time ago, when I was just 21 years old, went to my house, with my parents.
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"When I saw you I said, 'he's the man who brought Zizou and Ronaldo and now he wants me in his team'. Thank you very much for that.
"I'll never forget Real Madrid because it is impossible. It's the best club in the world and in history, that's as good as it gets. It's time for me to leave today and to have another story, but the most important thing for me is what I've won here.
"It's a little bit of a sad day, because I'm leaving this club and that pains me. My dream was in my head, I signed for Madrid and I wanted to finish at Madrid, but life sometimes gives you another opportunity and I've taken it with all my family."
Benzema joined Los Blancos from Lyon in 2009 and won four LaLiga titles and five Champions League crowns.
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But a new challenge awaits the Ballon d'Or holder in the Middle East, which will see him join former Real Madrid teammate Cristiano Ronaldo, who plies his trade with Al Nassr.
Al Ittihad pipped Al Nassr to the Saudi Pro League title last month.