I work for an orthopaedic surgeon who specialises in knee surgery so even though it's not veterinary I might be able to offer some insight!! An osteotomy is a procedure involving reshaping of bone to give relief from injuries and also to stabilise a joint when necessary. Does your dog have a cruciate injury? This can be a painful condition but more often leads to joint instability so in your case I am assuming the surgery is being undertaken to repair the cruciate and stabilise the stifle.
Human recovery from a cruciate reconstruction/tibial osteotomy is about six to twelve months in total, with intial recovery being about three months. This is with a leg brace and rehabilitation, which I assume your dog has (or a plaster cast).
The reasons for this kind of surgery are not only for pain control and to restore stability but also to help ward off problems later in life such as osteoarthritis.
If your dog is young, healthy and active his recovery should go well, but you will need to keep him from doing too much with the leg for six weeks initially if possible! (though he should be weight-bearing almost immediately) A good thing about cruciate reconstruction (although osteotomies need a little more rest) is that exercise and rehabilitation and using the joint are the keys for a strong recovery - at least in humans!
Good luck and good on your for taking care of your dog so well.