I actually think your boss is creating a problem for you.
Of course it's taxable. The things IRS will look at (and they very well might, as it does stand out) what kind of payment is that.
Why did it not go through payroll? The company may be at risk here for avoiding FICA/FUTA/workers' compensation insurance/State payroll taxes. Some are mandatory, and cannot be left to the employee to pay.
On your side it raises your taxable income without the appropriate withholding, you may end up paying underpayment penalties for that (that is why you've been suggested to keep proofs of when you were paid).
Also, it's employment income. If it is not wages - you're liable for self-employment taxes (basically the portion of FICA that the employer didn't pay, and your own FICA withholding).
When you deposit the check is of no matter to the IRS, its when you got it that determines when you should declare the income. You don't have a choice there.
I suggest asking the company payroll why it didn't go through them, as it may be a problem for you later on.