Last year, the 66-year-old construction magnate won the backing of members for statute changes that make it harder for outsiders to seize control of the world's richest football club by income.
A potential presidential candidate has to have been a club member for at least 20 years, up from 10 years previously, and must personally provide a bank guarantee worth 15 percent of the club's budget - some 75 million euros - rather than relying on any third party.
Perez will be officially presented for another four-year term at the helm on Tuesday.
One of the first issues he will need to address will be to appoint a new coach after Jose Mourinho and the club agreed a parting of the ways, despite the Portuguese having three years left on his contract.
Paris Saint-Germain's Carlo Ancelotti and departing Bayern Munich boss Jupp Heynckes have been linked with the post in the local media.
In an interview with local newspaper ABC on Sunday, Perez said Real needed: "A coach who understands them well, and that we compliment the team with some improvements, but not many.
"The door isn't closed for Mourinho. He leaves saddened after struggling to understand what the media are like here."
Real have finished the season without a major trophy after coming in second behind arch rivals Barcelona in La Liga, falling in the semi-finals of the Champions League and losing the King's Cup final to city neighbours Atletico Madrid.
Perez was president between 2000 and 2006 when he was the architect of the 'Galacticos' policy that brought players such as Zinedine Zidane and David Beckham to the Bernabeu, before quitting mid-term.
He returned in 2009, after Ramon Calderon had been forced to step down accused of vote-rigging at a club general assembly.
Real are one of four Spanish top-flight clubs owned by their members, alongside Barcelona, Athletic Bilbao and Pamplona-based Osasuna.
