Benzema established himself as one of Europe's hottest properties during his time at Lyon, for whom he scored 54 competitive goals in the last two seasons, and he was regularly linked with some of the continent's biggest clubs.
Madrid won the race for the France international after having a 35 million euros (£25m) bid accepted by Lyon last week, but while Benzema insists the Spanish giants were always his top choice, he confirmed they were not his only suitors.
When asked what other teams were keen on him, Benzema said: "There were quite a few clubs that contacted me like Manchester (United), Inter Milan and Barcelona, but I decided to come here.
"Real Madrid are an excellent club. I've dreamt about playing here since I was 15 years old. Florentino (Madrid president Perez) spoke to me about the team and the project that he wanted to create. I wanted to play at Real Madrid anyway so he didn't have to convince me of hardly anything."
Benzema is the the fourth new arrival to be unveiled by the Spanish giants since Perez returned to the presidency at the start of June, following in the footsteps of Cristiano Ronaldo, Kaka and Raul Albiol.
An estimated 90,000 people turned up for Ronaldo's presentation at the Bernabeu on earlier this week, while around 55,000 were in attendance for Kaka's unveiling last week.
The amount of people that watched Benzema's presentation last night was considerably less than those two players, with around 20,000 in the stands, but the Frenchman was still delighted with his reception and immediately endeared himself to the fans by repeatedly kissing the Madrid badge.
"It was very exciting. Real Madrid fans have a special relationship with the players and I am very grateful for that," he said.
"I felt some strong emotions today and that's why I kissed the badge."
Benzema, who has not yet been given a shirt number at his new club, was a prolific scorer with Lyon and he is confident he can be a regular marksman at Madrid as well – if he can secure himself a place in what is promising to be a star-studded line-up.
"I don't want to promise a set number of goals, although I hope to score a lot. With players like Kaka, (Cristiano) Ronaldo and Raul it will be very easy for us to get goals," said Benzema, whose signing takes Madrid's spending this summer towards the £200 million mark.
"I'm aware that there is great competition at the club and maybe I cannot always play, but I've come here to fight, so it's not going to be a problem."