It is as stated a sole ownership/proprietorship business. I am already aware of the financial status and have been running the business for some time now but it has come time to actually transfer ownership.
You should speak to a business/corporate attorney to address the various issues you face in connection with the transfer as well as considering the creation of a LLC or corporation to operate the business and provide for some level of liability protection going forward. In addition, you may want to have someone with tax experience to assist in structuring the acquisition.
If there are any employees in the business, you definitely want to incorporate or form an LLC so that you are not personally responsible for the negligence of your employees and are not personally responsible for the contract liabilities of the business. You do have such responsiblity if you operate the business as a sole proprietor. Also, the transfer of ownership can take many forms, depending on the value of the business and whether your grandfather wants a fair market value sales price or is willing to give you a reduced price or gift the business to you since you are already running the business. I agree with the answers of the other attorneys that you need an attorney with experience in transferring businesses who can raise issues that you might not otherwise think about.
You should sit down with a corporate attorney to make sure that you get the proper documents evidencing the deal to transfer the business to you. Whether it's a purchase and sale or assignment agreement - you'll want to make sure that you are covered in terms of ownership, liability, etc.
It may also be a good time to discuss incorporating to get some liability protection that an LLC may offer. You don't have to do this, but with the transition already contemplated now may be a good time to go that route.