Swanson, 20, signed a contract until 2011 after sealing his move from Berwick Rangers on Wednesday.
The midfielder will move to Tannadice in January and Levein said he was confident the player would bolster the squad.
"We've got a solid base to from in midfield now, with the likes of Morgaro Gomis and Prince Bauben, so we've got the defensive side of it covered," he said.
"But Danny is more of an attacking player. Willo Flood is in there just now, but he's on loan and we have to be careful we don't get into a position where him going back leaves us with a big gap.
"We're looking ahead a bit so he's coming in to train with us to get to know the lads.
"He's a bit subdued at the moment, but that's to be expected and he'll get up to speed quickly."