Johnson, 27, has been the subject of reports linking him with a transfer away from St Andrew's, with his impressive performances during the past two seasons a key factor in Birmingham's success under McLeish.
After helping Birmingham to Carling Cup success last week, he said: "I'm looking forward to going forward with Birmingham. I have enjoyed it here and I am still enjoying every minute of it now.
"Moments like last weekend at Wembley were the reason why I came here. Now another big plus point in anyone's career will be playing in Europe. We will enjoy that when it comes around."
Johnson, who moved to Blues in a £5 million deal, added: "I knew the club was going in the right direction and, yes, I'm happy here. Until the manager wants me gone then I'm here."