On the monadicity of finitary monads

In 1993, Kelly and Power showed that the category of finitary monads on a locally finitely presentable category script A sign is of descent type over a power of script A sign; here we establish the stronger result that the forgetful functor in question is monadic. Both their result and ours remain true in the script V sign-enriched case for suitable monoidal categories script V sign. Generalizing further, we obtain a monadicity result for algebras for an operad.