How long should I expect to take anti-rejection medications after my kidney transplant?

Forever. If you stop the immunosuppression medicine your kidney will stop working.
Lifetime medication. You will need to take anti-rejection medications for life, or at least the life of the transplant. The dosages will be reduced some from the initial dosage but you will need meds to prevent rejection. The risk of rejection never goes away.
Lifelong. You will need to take your anti-rejection medications as long as the kidney continues to function.

Related Questions

How much time does it take to die after going off of kidney transplant anti- rejection meds?

Hard to say. Immunosuppression medications are necessary to prevent the body from attacking the transplanted kidney. If the medications are stopped, the body begins to attack (reject) the organ and the kidney will eventually fail. Once this happens, dialysis will need to be started. Many factors affect the rate at which the body attacks the kidney, making an exact answer to your question difficult.