Blues have high hopes for the Chilean winger, who they snapped up from Club America over the summer.
They believe the tricky winger will bring something different to their attacking arsenal and are confident he can make a positive impression.
McLeish is excited by the prospect of cutting Beausejour loose and feels the South American, along with fellow deadline day recruits Alexander Hleb and Martin Jiranek, will help to make Birmingham a more formidable proposition.
"Yes, we believe he (Beausejour) can perhaps provide us with something we haven't got," the Scot told the Birmingham Mail.
"He's quick, he's explosive, he can change pace. He's got a great delivery of crossed balls and he's very much a team player, in games that I've seen with Chile.
"The one game I saw, recently, against Man City with his club America, he certainly fits the bill.
"He looks hungry, he is desperate to show what he can do in the Premier League. I think we have signed three good guys."
Beausejour has limited experience of European football, but proved during this summer's World Cup that he has the ability to compete at the highest level.
"He had a tremendous World Cup," added McLeish.
"He was Chile's star player against Spain. He showed his speed and strength, and also throughout the tournament he would not shirk his other duties."