The Spanish Under-21 playmaker, who was joined from Malaga for some 30 million Euros, completed a medical and signed a five-year contract before being presented in front of around 5000 cheering fans at a sun-soaked Bernabeu on Wednesday.
"It's a great opportunity that is always in your head, and if I do things well here, I might have an opportunity to be in Brazil," Isco, who will wear the number 23 shirt, told a news conference.
Isco, 21, helped Malaga to a club best fourth-placed finish in La Liga two years ago and to the Champions League quarter-finals last season in their debut campaign.
He caught the eye with a series of impressive performances in the European Under 21 Championship in Israel last month, scoring a penalty in Spain's 4-2 final victory over Italy.
The talented midfielder was voted by coaches the 'revelation player' of La Liga two years ago and he won the 'Golden Boy' trophy as the best Under-21 player in Europe in 2012.
He debuted with the Spain's full national team in a friendly against Uruguay in February and is one of the popular choices to make the step up into Vicente del Bosque's side after their Confederations Cup final defeat to Brazil last weekend.
Isco was also a target for Manchester City and their new coach Manuel Pellegrini who worked with him at Malaga the last two seasons.
"I had offers from other clubs in Europe, but it is impossible to say no to Real Madrid," Isco added, when asked why he reportedly changed his mind from signing for City to join Real.
"I couldn't let the opportunity pass me by."
Isco will have to fight for a place in the Real starting line up but he was unperturbed.
"I have a lot of confidence that I will be able win myself a place here," he said. "No one will gift me minutes but I hope with hard work I will carve myself a niche."
There has been much speculation in the local media that Isco is a fan of Real's arch rivals Barcelona, fuelled by the fact he has a pet dog called Messi, named after Barca's World Player of the Year.
While he juggled the ball on the pitch at the Bernabeu, fans chanted for him to kiss the Real badge, which he failed to do, and he deftly sidestepped the question in the news conference.
"It's true I have been a Malaga fan, now I am the biggest Madrid fan there is. I will give my all for this shirt," he said.
When asked about his dog, he replied to much laughter: "Yes. But I also had one called [Luis] Figo. It is nothing more than an anecdote."
Former Portugal international Figo played for Barcelona and Real.
