Zuly linked to my previous answer on a similar question, but it's worth repeating here. I am not a lawyer but I've been through a similar situation and am passing on the advice I received:
If you operate any sort of business arrangement in the absence of a formal contract, then you are viewed as a "general partnership" in the eyes of the law. Under this arrangement, you have very strong, legally-binding fiduciary agreements to your partner. This basically means you have to look out for his best interests, as he has to look out for yours.
There's a common myth among founders that -- if you haven't signed anything -- you don't owe anyone anything. This is 100% false.
Your best bet is to convince him to agree to leave the business, and get it in writing. These types of documents are called "Releases." At minimum, it should say that:
- he assigns all of the businesses assets to you
- he forfeits all intellectual property rights
- he forfeits all claims to the business in perpetuity
- he won't misrepresent himself as an agent of your business
It'll take lots of coaxing -- you'll probably have to give him money -- to get him to sign this release. The best way to do it is to sit down with him, work out what you both think the business is roughly worth, and then offer to pay him half (from your own personal money, not the business's). It's important to keep in mind that it must be an amicable agreement. If he gets cold feet, then you've only created bad blood, and you're still stuck with him.
It might sound impossible, but it's necessary. If you don't get him to sign, he'll turn into a huge liability for your business. No VC will want to invest in a company if they know that there's an estranged ex-co-founder out in the wild who could decide to sue the business for 50% of its assets whenever he wants.
Not only will he tank your deals, but it will absolutely ruin your relationship with him. There'll be intense bitterness and resentment and it will only get stronger as you grow more successful. You need to reach an agreement that you're both comfortable with, as soon as possible.
If you can't get him to sign, then you need to give up on the business and find something else. It's virtually impossible to build a successful business knowing that an estranged and bitter co-founder is out there.
Have a lawyer look over the document before you present it. You have to play softball as much as you can and be willing to pay him a lot. If he walks away from the agreement, you're screwed. You can't let that happen. Put on your happy face and genuinely try hard to work something out.