The changes, approved at a general assembly in Madrid on Sunday, will mean presidential candidates will have to have been club members for at least 20 years, up from 10 years.
They must also personally provide a guarantee worth 15 percent of the club's budget - around 75 million euros - rather than relying on any third party as has sometimes happened in the past.
A construction magnate and one of Spain's richest men, Perez told members he had nothing against "sheikhs or Russians" and was attempting to protect the club and its 70,000 members, who legally own the Spanish champions and elect the president.
"Sincerely, not just anyone can come here and take over the club, however much gift of the gab he has, and run it into the ground," Perez said.
"This is not a petanque club, it's the most important sporting institution in the world," he added.
"If a sheikh, a club member, wants to provide the guarantee let him come and do it, but it must be in his name.
"A third party cannot guarantee a candidacy because it is against the spirit of sport and against us.
"I don't want to think badly of anyone but this is a matter for our members and not outsiders."
Perez is moving to shore up Real as its annual revenues soared above half a billion euros for the first time in the 2011-12 season.
Real made 514 million euros, up seven percent from the previous season and the most of any sports club, and returned a post-tax profit of 24.2 million, Perez said.
Net debt had shrunk to 124.7 million euros from 169.7 million and projected revenue for 2012-13 was 517 million, he added.
"There is no sports club, not in soccer or any other sport, that reaches this level of turnover," the 65-year-old said.
"Our economic leadership is a guarantee that we will maintain institutional stability and that we will remain in charge of the club."
Perez also gave details about the project to remodel the club's giant Bernabeu stadium in central Madrid and said the board were considering four proposals, all of which would include covered seating for the whole stadium.
Work was projected to begin after the end of the current season and would take three years.
"Our stadium is key to our identity and that's the reason we want to place it in the very front rank, transforming it into a global architectural icon."