A murderer has three rights on him. That of Allah, that of the murdered person, and those of his or her immediate kin.
As for Allah's right it cannot be requited but with true repentance.
The right of the immediate kin can be requited by the murderer by handing himself over to them in order that they either: a) turn him over to the authorities for execution; b) accept monetary compensation from him; or c) forgive him.
The right of the person himself who was murdered cannot be compensated for in this world. Some scholars are of the opinion - and this seems to be the preferable opinion - that if the murderer is true in his repentance, Allah will clear him of his sin and compensate on his behalf by satisfying the person murdered on the Day of Judgment.