Benzema said: "In my head it was clear that I wanted to continue my progression here and not exile myself in Spain, England or Italy.
"Everyone has faith in me, my team-mates are behind me. I really want to win lots of titles, starting with a cup-league double this season and I'd love to one day win the Champions League with Lyon. There's still so much to do."
Although the five-year contract is the maximum length that can be offered, Benzema did not say that he would stay in France for its duration.
"I can't say how long I'll be here, maybe another two or three years," he added.
"The moment will come, we'll decide it together with the president."
Club president Jean-Michel Aulas, meanwhile, admitted that the club had had to put its hands in its pockets to ensure that their star player was not attracted by lucrative offers from abroad.
"With sporting ambition comes financial ambition," he explained.
"We've done what we thought was necessary so Karim wouldn't be embarrassed to compare what he gets with what he would have got abroad.
"We've done the most possible, he completely deserves it. It was necessary that he not only felt good here but that he had the salary he deserves with his talent, which is immense. We're staking a lot on him."