Spurs have reinvested some of the money received from Bayern Munich for Harry Kane on the 22-year-old Wales international, who scored eight goals and provided three assists to help Nottingham Forest avoid relegation last season.
Johnson was not registered in time to feature in Saturday's 5-2 thrashing of Burnley at Turf Moor, but his arrival should add another dimension to a Tottenham side who were inspired by Son Heung-min's hat-trick and could have scored even more in an exciting attacking display.
“He's just another exciting young player,” Postecoglou told reporters.
“He's a real threat in the front third, he's different from what we've already got, he's young and ambitious. It's no secret that's the model for me.
“It's just as much about the person as well as the footballer, and looking at him he's going to fit in really well with this group. He's ambitious and hungry and wants to take his game to the next level.
“The technical and the physical attributes he has, he should fit in really well.”
Johnson was the ninth signing of a busy window for Tottenham, who spent more than £200m to reshape the squad in Postecoglou's style.
But the Australian said it was just the start and that there is more work that he wants to do in in future transfer windows.
“When you look at the team we have now, we virtually changed half the starting line-up, the way we train, the way we coach,” he said.
“The rebuild was never going to be one window.”