An exclusive anti‐Markovnikov hydroamination as well as hydroalkoxylation of allylic alcohols catalyzed by a simple catalyst Y(CH2SiMe3)3(THF)2 has been developed, providing a variety of γ‐amino and γ‐alkoxy alcohols in good yields under mild conditions. Moreover, this protocol is applied to the synthesis of drug molecules Propipocaine and Proroxan. The rare‐earth catalyst features readily available, wide substrate compatability, exclusive anti‐Markovnikov selectivity, and performs in the absence of a base or an additive.