OP: The part or the rear hub that the cassette slips onto is called the freehub. Campy freehubs and Shimano freehubs are different and are not compatible. In other words, you can't put a Campy cassette on a Shimano freehub and vice versa.

Based on what you've written, your current bike's drivetrain (shifters, derailleurs, chain and cassette/freehub) is Shimano. You recently purchased a new set of wheels with a Campy cassette (and therefore a campy free hub). As others have pointed out, this is not compatable with your bike's drivetrain.

American Classic makes a "conversion" cassette that has campy cogs/spacing, but fits on a shimano freehub. If you're REALLY lucky, this is what is on your new wheel, but I doubt it.

Unfortunately, what you would be looking for is the opposite - a conversion cassette that adapts a Shimano type cassette to a campy freehub. I don't know if such a thing is available.

You can however change your new wheels' freehub from campy to shimano, but others with more expertise will have to chime in on that. I don't believe it's a huge deal cost or effort.