All legal and ethical aspects aside, if you want to keep it you need to launder it. Doing so is simple: Start *living* on a small portion of that money every month. Use it to buy gas or groceries or whatever. Make sure to also use your bank account to purchase those items here and there.
Since you won't be spending as much from your checking account each month, you'll have extra to move over into a savings account.
Voilà, you have deposited the money in the bank without really doing so.
Should all work out until you find out those are marked bills from a kidnapping/ransom/murder case and you end up in the middle of it.