While the answer to a riddle can simply be called an answer, the term "solution" is also applicable. Either term is usually acceptable, although the type of riddle helps delineate which word is best for the riddle in question.
Riddles are often posed as questions. The answer to a question riddle is usually referred to as the riddle's answer. When the riddle is referred to as a "problem," such as in mathematics, the term "solution" is typically more appropriate. The answers to riddles posed as poems are also often called "solutions."
The term "riddle" comes from the Old English term for interpretation or opinion.