A cadaver tendon will be used to surgically repair one of my tendons. Is this the same as a heart transplant, where you then have to take pills to stop your body from rejecting the foreign tissue?
The short answer is: No, you will not have to take pills to stop your body from rejecting the foreign tissue.
What you are talking about is an allograft (Greek allos = "other") from another individual.
Before you receive the cadaver tissue as a graft, it will have been subjected to techniques such as freeze-drying, gamma-irradiation, and chemical sterilization.
Each of these methods effectively removes the extracellular markers that prevent your immune system from attacking the allograft.
The graft may fail for other reasons, but not because of an acute immunological rejection.