Will I have to take medications the rest of my life after my kidney transplant?

Yes. Since the donated kidney is a "foreign" tissue, your body will reject the organ unless you suppress your immunity to some degree. These medications called immunosuppressants are generally required for lifetime but amount may decrease over the years.Your doctor monitors and determines the type and dose.
Kidney's lifespan. The transplanted kidney will always be genetically different from your body. Your immune system will always recognize the txp as a foreign invader + try to destroy it - this is rejection. Today, our preventive medications can only temporarily lower the immune system's ability to reject. Soon after they are stopped rejection will probably occur. Someday longer acting strategies will hopefully work.
Yes. As long as the transplanted kidney continues to function, you will need to take your anti-rejection medications. Some patients think their immune system might get used to the transplanted kidney but this is UNTRUE. If you stop taking your anti-rejection meds, you will end up with a rejection and will put the kidney at risk.