It's a big step to get rid of your blades. Well done on doing something so huge and powerful! :).
I currently keep my tools around, but I have gotten rid of them before. It was definitely scary and a little sad--like I was saying goodbye to an old friend. However, it was freeing not to have to worry about my family discovering/moving them. Also the temptation to self-harm is greatly reduced, simply by not having tools around. It breaks the cycle of self-harming because they're there and feeling guilty about it later.
The healthcare professional in me says that ideally, sharp objects contaminated by blood should be disposed of in a Biohazard container. However, that's probably not an option for you. If your blades have no cover or cap, securely wrapping them in an old towel (and taping it tightly shut) should help protect other people from being accidentally cut by them when you throw them out. Then just put them in a trash can, away from your house if you need to. In addition, it will make the process more final.
Good luck, and let me know how it goes!