The Chile World Cup star is a different kind of winger to those already at his disposal.
Beausejour, signed from Mexican side Club America for around £3.3 million, is more of a throwback.
"Yes, we believe he can perhaps provide us with something we haven't got," admitted McLeish to 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 the 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."