Johnson quickly made his presence felt while Dann has had to wait until the last month to make his mark with Blues after injury problems.
But the pair have looked increasingly at home with life in the Premier League and will now try and block out Liverpool in Monday night's Premier League clash at Anfield.
McLeish said: "I am not surprised how well Johnson and Dann have done. I think it shows we felt our homework was right about the players.
"I have to admit we did look at centre-halves with Premier League experience but, in the end, it was too expensive.
"I turned to the centre-halves whom I believed were as good as anyone, if not better, than anyone in the Championship in Johnson and Dann and they had that potential in them to do well.
"With the type of mentality they have got, they are winners. They will throw themselves at the ball on the edge of the box. You saw the bravery of Roger against Manchester City last weekend when he took a real painful knock in the throat.
"These two boys really want it. I know they want it, want to do well, learn and succeed, and there is a lot ahead of them.
"But they know the real proof of the pudding is if we our retain Premier League status and they've both been a big part of achieving that, in being mainstays and the rocks around which we've built the team.
"Then they will know they've arrived as Premier League players - but I've been pleased with them so far."
McLeish believes Birmingham can go to Anfield full of confidence after impressive displays in the last two games with Sunderland and Manchester City have yielded four points.
He said: "The last couple of performances gives the players the entitlement to believe in themselves. They have played some good football this season.
"I don't know what the fans feel about our overall season, but I am sure they have seen some pretty decent football from the team regardless of what system we have played - from the first kick of the season to this very moment.
"We know face another huge challenge, and the players are going to Anfield feeling good about themselves, but we know it is a game where we are ranked as underdogs."
Birmingham midfielder Barry Ferguson is suspended after being sent off for two bookable offences against Mark Hughes' side.
On-loan keeper Joe Hart is available after being ineligible to face his parent club although his deputy, Maik Taylor, produced an impressive performance.
Winger Keith Fahey is battling to overcome a knock to his knee in training but striker Garry O'Connor is still troubled by a groin problem.