Blues boss McLeish is delighted to have funds at his disposal but will not allow other clubs to take advantage of his new found spending clout.
He said: "We will not be held to ransom and pay over the odds because that is the road to ruin.
"If, for example, we are competing with a club and have to pay a little bit more to acquire a player we want, then we may look at that - but not if the selling club decide to double the price.
"I think we still have to realise we are not Manchester City, Manchester United, Liverpool. Let's not get carried away with ourselves.
"We will still target a certain type of player but I know there are players out there who can enhance my first eleven and they would be within reasonable parameters.
"But we are not going to go out and look for an Adebayor all of a sudden. I come from a prudent background and worked at clubs where I turned the lights off in every room."
Yeung's immediate target is to ensure Blues stop yo-yoing between the Coca Cola Championship and the Premier League after two relegations and two promotions in the past four seasons.
He said: "What is the target for Birmingham? Maybe 10th or ninth this season, maybe better next season, not to be a yo-yo club anymore.
"Our aim is to work hard to secure our position in the Premier League, not only for this year but for many years to come.
"It's a long, long target but we hope Birmingham can become one of the best clubs in Europe. Let's take it step by step - but why not? We want to be as big as possible."
Yeung has also given his backing to former Scotland boss McLeish and said: "I am very confident in Alex. He is a good coach and a good leader."
Yeung acquired 29.95% of the shares in City two years ago in becoming their largest individual share-holder but has had to wait until now to assume full control.
He said: "I'm happy to be here. It has taken a long time to buy the club - but finally I have got it."