Zingarevich's Thames Sports Investment group completed the initial stage of their takeover on Tuesday following ratification by the Premier League and Football League.
It followed a drawn-out investigation into the 30-year-old Russian's background, a process that took longer than expected and raised concerns about the chances of the deal going through.
Zingarevich's father, Boris, and TSI's Chris Samuelson were both involved in a proposed buyout of Everton that collapsed at the 11th hour back in 2003.
However, neither the Premier League nor the Football League saw any grounds for concern following the outcome of their 'fit-and-proper-persons' test designed to stop clubs from falling into the wrong hands.
Speaking exclusively to the Chronicle, Madejski, 71, said: "Everyone is looking for demons that half the time don't exist.
"Our fans, like I am, should be eternally grateful that Anton is coming to the club. He has the ambition to take us forward.
"We're in the Premier League and on the brink of something really exiting happening. I just want people to enjoy that and look to the future."
The £25 million buy-out will give TSI more than a 51% stake, the figure widely bandied about in the media since Zingarevich first announced his intentions back in February.
"There are good guys and bad guys - and we've got a good guy," Madejski insisted. "What I don't want is to dwell on negatives when we have done something spectacular here. It's not fair to the new owners to start saying negative things about them, they deserve a chance.
"Not only that, but people are generally too ready to be negative about things. Let's be positive about it instead.
"We are in the Premier League now thanks to Anton Zingarevich and we're going forward with a great manager and a great squad.
"We've also got excellent staff here so let's be excited about this and not go looking for reds under the bed because they don't exist."
And he added: "I can understand why the process took a bit longer than expected. But I think it's rather sad when everyone gets tarred with the same brush, and most of the time unfairly.
"But the fact is I'm pleased that much scrutiny took place and everyone is happy with us moving forward. It's a win-win situation."
Madejski says he also expects former Bearwood College pupil Zingarevich to gain total control of the club within the next 12 months.
Zingarevich's plans involve increasing the capacity to Madejski Stadium to 38,000 and selling the naming rights.