The procedure that stiffens a joint by joining two bones is

arthrodesis

Explanation:

Arthrodesis is also known as artificial ankylosis ans is a surgaical method to fuse the bone in a joint. This method is used when all other methods are not working and is mainly opted in case mobility of joint is affected. Arthrodesis is a painless method unlike the other joint related surgical methods. It provides a more permanent solution to joint related issues as the replacement joints implanted have the same level of motion as that of natural joints and hence it is a more viable solution as compared to other joint replacement surgeries.