Johnson is the third centre-back to be signed by Blues boss Alex McLeish this summer after Scott Dann and Giovanny Espinoza and the fee is a club record for a defender.
But he told Birmingham's official website: "Competition (for places) is good. We had it at Cardiff when I first signed and I had to battle my way into the side.
"I am not frightened to do that. I am not expecting to walk into the side. I will battle it out with the other boys and I am sure they are thinking the same."
As regards the fee, Johnson said: "The fee in a way does add a bit of pressure, but I will just do what I do.
"It is a massive fee but I take pressure in my stride and just crack on. Hopefully I will do as well as I did at Cardiff and do the same for Birmingham."
With the new season a little over two months away, Johnson is relishing pitting his wits against the top players of the Premier League.
He said: "I have played in an FA Cup final and I just want to play Premier League football. I am just looking forward to getting out there and playing.
"It will be amazing to go to Manchester United on the opening day of the season and hopefully I will be in the starting line-up but, as I keep saying, I just can't wait to start playing for Birmingham City."