Just hours after the being sworn in, the club also announced former Argentine striker and coach Jorge Valdano as its director general.
There was no official word from Real on a new coach, but Chilean Manuel Pellegrini, who has transformed the fortunes of Villarreal, was tipped to take over from Juande Ramos, who was handed a six-month contract in mid-December.
"The two clubs understand each other well and an agreement has been reached," said Villarreal director general Jose Manuel Llaneza, adding no contract has yet been signed.
Pellegrini, 55, is under contract with Villarreal until 2010.
In a speech on taking office Monday, the 62-year-old Perez vowed to build "the best club of the 21st century.
"We will devote all our effort to building a spectacular team with great players who are role models on and off the pitch. A club where ethics are indestructible and where solidarity will be a basic cornerstone of behaviour," he said.
The construction magnate is retaking the reins of Real, Spain's historically most successful team and the world's richest football club by revenues, for the next four years after standing unopposed in elections for president.
Real had been led on an interim basis by Vicente Boluda after Ramon Calderon stepped down in January following allegations that he rigged voting at the club's last annual general assembly in December.
Perez led Real from 2000 to 2006, when it earned the nickname "Los Galacticos", winning the Primera Liga twice and European Champions League with such stars as Zidane, Ronaldo, Luis Figo, David Beckham and Michael Owen.
Zidane's transfer from Juventus in 2000 cost Real a world record 75 million euros.
Perez had promised to give both Zidane and Valdano senior positions at Real if his comeback bid was successful. Valdano had acted as Real's sports director during his last term in office.
He has not mentioned any names regarding top signings but Spanish media speculate that Manchester United's Portuguese winger Cristiano Ronaldo, Liverpool's Spanish star Xabi Alonso and AC Milan's Brazilian playmaker Kaka are all his sights for next season.
"We must recover the dreams, stability and lost time," said Perez. "The road ahead will be difficult, but we have the passion and necessary ideas to overcome the great challenges of this complicated time."
Perez had quit Real in 2006 after the club went a third straight season without a trophy, its worst run in more than half a century, but he has remained popular with supporters.
Real finished second in La liga and exited the first knockout stage of the Champions League for the fifth straight season.
It ended the season on Sunday with a 2-1 loss to lowly Osasuna.
Source: AFP Global Edition