The striker, who had completed his medical earlier on Tuesday morning, signed a five-year contract and was handed a No. 9 shirt by club president Florentino Perez.
"Wow," Mbappe said in Spanish to roars from a packed Santiago Bernabeu Stadium.
"For years I've dreamed of playing for Real Madrid and today my dream has come true," said the 25-year-old former Paris Saint-Germain player.
"I'm a happy boy. I'm going to give my life for this club," said Mbappe.
Accompanied by his parents watching from the crowd and with a former French hero of the club, Zinedine Zidane, in attendance, Mbappe was emotional as the crowd chanted his name, and at one point kissed the jersey of the reigning Spanish and European champions.
Mbappe is "an exceptional player who comes to help us continue winning, a player who today fulfils the dream of his life," said Perez. "Welcome to your home."
Exciting offensive trio
Although his new teammates began training on Monday, the forward, who captained France during their unsuccessful Euros campaign, will have a few more days off before kicking off his season in the Spanish capital.
The unveiling of Real's latest Galactico allowed its fans to continue celebrating following Spain's Euro 2024 triumph on Sunday.
The crowd was expected to be bigger than that 15 years ago when Cristiano Ronaldo was unveiled.
The free tickets were snapped up rapidly with some fans reportedly trying to resell them to take advantage of the hype surrounding the arrival of arguably the world's best striker.
At Real, Mbappe will form part of an offensive trio alongside England midfielder Jude Bellingham and Brazil attacker Vinicius Junior under the watch of veteran Italian coach Carlo Ancelotti.
That prospect is already exciting fans of the club who won their 15th Champions League title in June.
Los Blancos begin the defence of their La Liga crown with a match against Real Mallorca on the weekend of August 17-18.
Mbappe's debut might have to wait until the following week when Real Madrid face Real Valladolid who were recently promoted from the second division.
Number 9 Mbappe shirts went on sale last Thursday in Real's club shops which are covered with his image.
Mbappe arrives after a personally disappointing Euros campaign, where he was overshadowed by Spain's new teenage sensation Lamine Yamal of Madrid's rivals Barcelona and France lost to Spanish in the semi-finals.
That followed a difficult season with PSG following his decision not to renew his contract, with the striker -- who was the Paris club's all-time top scorer -- admitting he felt "liberated, relieved" by his transfer to Real.
The club is hoping to offset the costs -- a salary of at least 15 million euros ($16.3 million) per season and a signing bonus of more than 100 million euros -- through sponsorship deals and ticket and merchandise sales.
Mbappe is hoping the move will finally see him win a Champions League and the Ballon d'Or, two of his lifelong objectives.
